Rock is tossed upwards with an initial velocity of 80 ft/sec from an initial height of 150 ft . The values of a, b, and c are: a = 8, b = 100, c = -100.
To find the values of a, b, and c, we need to use the given information and the position function s(t) = at² + bt + c.
First, let's find the values of a and b. We know that the rock was tossed upwards with an initial velocity of 80 ft/sec, which means that the initial velocity component in the vertical direction is 80 ft/sec. Since we are assuming that the only force acting on the rock is gravity, we can use the kinematic equation:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity (-32 ft/sec²), and t is the time elapsed. At the highest point of the trajectory, the final velocity is 0 ft/sec (the rock momentarily stops before falling back down), so we can set v = 0 and solve for t:
0 = 80 - 32t
t = 2.5 sec
Now we can use this value of t to find the height of the rock at the highest point:
s = ut + (1/2)at²
s = 80(2.5) + (1/2)(-32)(2.5)²
s = 100 ft
Therefore, the highest point of the trajectory is 150 + 100 = 250 ft above the ground.
Since the rock starts at an initial height of 150 ft and reaches a maximum height of 250 ft, we know that the vertical displacement of the rock is 100 ft. We also know that the time taken for the rock to reach its highest point is 2.5 sec. Using these values, we can find the value of a:
s = ut + (1/2)at²
100 = 0(2.5) + (1/2)a(2.5)²
a = 8 ft/sec²
Now that we have found the value of a, we can use it to find the value of b:
b = u + at
b = 80 + 8(2.5)
b = 100 ft/sec
Finally, we can use the values of a, b, and the coordinates of the vertex (2.5, 250) to find the value of c:
s = at² + bt + c
250 = a(2.5)² + b(2.5) + c
c = 150 - a(2.5)² - b(2.5)
c = 150 - 50 - 200
c = -100 ft
Therefore, the values of a, b, and c are:
a = 8, b = 100, c = -100
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"Analyze the graph, with a detailed explanation tell me why you chose your answer.
Example: The answer to the given problem is ___. I chose this answer because, after analyzing the graph _______. "
The average speed of this object having a graph like this is
10/5 = 2 meter/minute. Because this object changes distance of 10 m in 5 minutes of time. Hence option B is correct.
Speed is a rate of change of distance with respect to time. i.e. v=dx÷dt. Speed can also be defined as distance over time i.e. speed= distance ÷ time it is denoted by v and its SI unit is m/s. it is a scalar quantity. Speed shows how much distance can be traveled in unit time.
To find dimension for speed is, from formula Speed = Distance ÷ Time Dimension for distance is [L¹] , Dimension for Time is [T¹], Dividing dimension of distance by dimension of time gives, [L¹] ÷ [T¹] = [L¹T⁻¹] Dimension for speed is [L¹T⁻¹].
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7. Assuming electrical energy costs 0.080 dollars per KW.h, calculate the cost of running each of
the following appliances for 24 h if 115 V is supplied to each:
a. A 75 W stereo
b. An electric oven that draws 20 A of current.
c. A television with a resistance of 60 ohms.
Assuming electrical energy costs 0.080 dollars per KW.h, calculate the cost of running each of the following appliances for 24 h if 115 V is supplied to each then A 75 W of power stereo will cost and an electric oven that draws 20 A of current will cost . A television with a resistance of 60 ohms will cost
For a
Power P = Work/time
putting values,
75 W= Work/24h
Work = 1.800 kW-hr.
Cost = 0.080×1.800 W-hr.
Cost = 0.114 Doller.
b)
P = VI = 115*20 = 2300 W = 2.3 kW
Work = 2.3*24 = 55.2 kW-hr
cost = 0.08*55.2 = 4.4 Doller
c )
P = V²/R
P = 115²/60
P = 220.6 W = 0.22 kW
Work = 0.22kW * 24 = 5.28 Doller
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10. a record player rotates at 45 rpm. how fast in m/s is a speck of dust 4.0 cm from the axis of rotation moving?
Answer:
The speed of the speck of dust would be approximately 0.188 m/s
Explanation:
We can use the formula:
v = ωr
where:
v = linear velocity
ω = angular velocity
r = distance from the axis of rotation
Firstly, we need to convert the angular velocity from rpm to rad/s. We can do this by multiplying the rpm value by 2π/60, which is the conversion factor for rpm to rad/s:
ω = 45 rpm × 2π/60 = 4.71 rad/s
Next, we can add the calculated values into the formula:
v = ωr = (4.71 rad/s)(0.04 m) = 0.1884 m/s
Rounding up to 3 decimal places, the speck of dust is moving at approximately 0.188 m/s.
when a battery is connected to a complete circuit, charges flow in the circuit almost instantaneously. explain.
When a battery is connected to a complete circuit, charges flow almost instantaneously due to the electric field established within the circuit components.
The battery acts as an energy source, creating a potential difference or voltage across its terminals. This potential difference drives the movement of charges, typically electrons, within the circuit.
Electrons experience a force from the electric field, causing them to move from the negative terminal to the positive terminal of the battery. As electrons flow through the circuit, they encounter resistance in the form of various components such as resistors, capacitors, and inductors. Despite this resistance, the charges continue to flow, allowing the circuit to function.
The flow of charges, or current, is maintained by the battery's continuous supply of energy. The speed at which charges flow is determined by the properties of the circuit, such as the resistance and capacitance. Although the flow of individual electrons may be slow, the electric field itself travels at nearly the speed of light. This allows for the almost instantaneous flow of charges within the circuit.
In summary, when a battery is connected to a complete circuit, the electric field established by the potential difference across the battery terminals causes charges to flow almost instantaneously throughout the circuit. The flow of charges encounters resistance from circuit components but is maintained by the continuous energy supply from the battery.
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if these stars are both 500 light-years away from earth, how will their apparent brightness compare?express your answer as an integer.
The main answer is that their apparent brightness will be the same.
This is because the distance of 500 light-years is the same for both stars, so the amount of light that reaches Earth from each star will be equal.
An explanation of this answer is that the brightness of a star is determined by its luminosity (how much light it produces) and its distance from Earth (how much of that light reaches us).
If two stars have the same luminosity but different distances, the closer star will appear brighter because more of its light reaches Earth.
However, if two stars are at the same distance from Earth, they will appear equally bright regardless of their luminosity.
In summary, if two stars are both 500 light-years away from Earth, their apparent brightness will be the same.
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Which of the broad area of I-O psychology interest you the most and why?
The I & O Psychology researchers are most interested in areas such as personnel selection, job analysis, performance management, organizational development etc..
What are different areas of interest in i & O Psychology?The personnel selection is a critical area that involves developing methods to identify the most qualified candidates for job positions. This area encompasses techniques such as job analysis, interview strategies and personality assessments.
Another area is performance management which involves developing effective performance appraisal systems, feedback mechanisms and coaching strategies to enhance employee performance. These are examples of diverse areas of interest within Industrial and Organizational Psychology.
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based on its surface temperature of 6,000 k, most photons that leave the sun's surface lie in which region of the electromagnetic spectrum? based on its surface temperature of 6,000 k, most photons that leave the sun's surface lie in which region of the electromagnetic spectrum? infrared x-ray visible ultraviolet microwave
Based on the surface temperature of the Sun, which is approximately 6,000 K, most photons that leave its surface lie in the visible region of the electromagnetic spectrum.
The distribution of photons emitted by an object depends on its temperature. The Sun's surface temperature of 6,000 K corresponds to a peak emission in the visible region of the electromagnetic spectrum. According to Planck's law of black-body radiation, as the temperature of an object increases, the peak wavelength of its emitted photons shifts to shorter wavelengths.
The visible region of the electromagnetic spectrum encompasses the range of wavelengths that are detectable by the human eye, approximately 400 to 700 nanometers (nm). The Sun emits photons across the entire electromagnetic spectrum, but the majority of photons emitted from its surface lie within the visible range. This is why we perceive the Sun as a source of visible light.
While the Sun emits photons in other regions of the spectrum, such as ultraviolet, infrared, and even some X-rays and microwaves, the bulk of the photons leaving its surface fall within the visible range. This is why we primarily observe the Sun's light as visible light.
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When blue light of wavelength 470 nm falls on a single slit, the first dark bands on either side of center are separated by 53.0 ∘.Part ADetermine the width of the slit.
When blue light of wavelength 470 nm falls on a single slit, the first dark bands on either side of center are separated by 53.0 ∘ The width of the slit is 1.63 µm.
The first dark bands on either side of the center of a single-slit diffraction pattern are known as the first-order minima. The angle between the central maximum and the first-order minimum is given by:
sinθ = λ / (a)
where λ is the wavelength of light, a is the width of the slit, and θ is the angle between the central maximum and the first-order minimum.
We can rearrange this equation to solve for a:
a = λ / sinθ
Substituting the given values:
λ = 470 nm = 4.7 × 10⁻⁷ m
θ = 53.0° = 0.925 radians
a = (4.7 × 10⁻⁷ m) / sin(0.925) = 1.63 µm
Therefore, the width of the slit is 1.63 µm.
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situation 1: a battery is used to power a cell phone. situation 2: the sun shines on a plant. is energy being transferred in either of these situations?
Yes, energy is being transferred in both situations.
In situation 1, the battery is providing electrical energy to the cell phone, which is then converted into various forms of energy such as sound, light, and radio waves to power the phone's functions. The chemical energy stored in the battery is being transformed into electrical energy, which is then transformed again into other types of energy.
In situation 2, the sun is providing radiant energy to the plant, which is then converted through photosynthesis into chemical energy that the plant can use for growth and survival. The energy from the sun is absorbed by the plant's chlorophyll, which transforms it into chemical energy in the form of glucose.
Both situations involve the transfer of energy from one form to another. In the case of the battery, chemical energy is transformed into electrical energy, while in the case of the plant, radiant energy is transformed into chemical energy. These transfers of energy are essential for the proper functioning and survival of both the cell phone and the plant.
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in an l-r-c series circuit te the phase angle is 53 and the source voltage lags the current. what is the current amplitude in the circuit.
In an LRC series circuit, the phase angle is 53 degrees and the source voltage lags the current. The current amplitude in the circuit can be calculated using the formula:I = V_s/X
where I is the current amplitude, V_s is the source voltage, and X is the reactance of the circuit. In an LRC series circuit, the total reactance is given by:
X = R + j(X_L - X_C)
where R is the resistance of the circuit, X_L is the inductive reactance, and X_C is the capacitive reactance. The phase angle of the circuit is given by:tan(φ) = (X_L - X_C)/R
In this case, because the source voltage lags the current, the phase angle is positive, so we have: φ = 53 degrees
Using the above equation, we can solve for (X_L - X_C)/R:
tan(53) = (X_L - X_C)/R
(X_L - X_C)/R = tan(53) = 1.327
Substituting this value into the expression for X, we get:
X = R + j(X_L - X_C) = R + jR tan(53) = R(1 + j tan(53))
The reactance of the circuit is therefore X = R(1 + j tan(53)).
The current amplitude can now be calculated using the formula:
I = V_s/X = V_s/(R(1 + j tan(53))).
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a 4.0 kg-block attached to a 20 n/m-spring constant spring moves on a frictionless horizontal surface, back and forth between -6.0 m and 6.0 m. what is the period of this motion, in seconds?
4.0 kg-block attached to a 20 n/m-spring constant spring moves on a frictionless horizontal surface, back and forth between -6.0 m and 6.0 m. The period of the motion is 4.4 seconds.
The period of the motion can be determined using the equation
T = 2π√(m/k),
where T is the period, m is the mass of the block, and k is the spring constant.
In this case,
m = 4.0 kg and k = 20 N/m.
Plugging these values into the equation gives T = 2π√(4.0 kg / 20 N/m) = 4.4 seconds.
Therefore, the period of the motion is 4.4 seconds.
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you see the moon rising, just as the sun is setting. what phase is the moon in? choose one: a. full b. waning crescent c. new d. third quarter e. first quarter
The moon is in the "new" phase when it rises just as the sun is setting. During this phase, the moon is not visible or appears as a thin sliver due to being positioned between the Earth and the sun.
When you see the moon rising just as the sun is setting, the phase of the moon is "new." During this phase, the moon appears dark and barely visible since the sun is illuminating the side of the moon that faces away from us. The moon is positioned between the Earth and the sun, with the sunlight falling on the side of the moon that is not visible to us. As a result, the new moon phase marks the beginning of the lunar cycle and is characterized by the absence of visible illumination on the moon's surface when observed from Earth.
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if you and a friend are on opposite sides of a hill, you can communicate with walkie-talkies but not with flashlights. explain.
When you and your friend are on opposite sides of a hill, the hill is blocking the direct line of sight between you and your friend. The radio waves transmitted by the walkie-talkie, however, are able to pass through the hill and reach your friend.
This is because radio waves have a longer wavelength and lower frequency than visible light, and are therefore better able to diffract (bend around obstacles) and penetrate through obstructions.
On the other hand, visible light (which is what flashlights emit) has a shorter wavelength and higher frequency than radio waves. Because of this, it tends to travel in straight lines and is easily blocked by obstacles like hills. When the light hits the hill, it is absorbed or scattered in different directions, so it does not reach your friend on the other side.
Therefore, while the walkie-talkie signals are able to travel over the hill and reach your friend, the flashlight beam cannot pass through the hill and will not reach your friend.
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gamma rays are group of answer choices he nuclei. high-energy electromagnetic radiation. positrons. h nuclei. electrons.
Gamma rays are a group of high-energy electromagnetic radiation .
Gamma rays are a group of high-energy electromagnetic radiation, which are produced by the decay of atomic nuclei or other high-energy processes such as supernova explosions.
Gamma rays have the highest frequency and shortest wavelength in the electromagnetic spectrum, and they are highly penetrating and ionizing, meaning they can strip electrons from atoms and molecules as they pass through matter. Gamma rays can be harmful to living organisms, and can cause damage to cells and DNA.
Therefore , precautions are necessary to limit exposure to gamma rays in certain situations, such as in medical imaging or nuclear power plants.
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what range of electromagnetic radiation is emitted when transitions from higher levels into n = 1 occur in a hydrogen atom? visible infrared microwave ultraviolet x-ray
The range of electromagnetic radiation emitted when transitions from higher levels into n = 1 occur in a hydrogen atom includes ultraviolet, visible, and infrared radiation.
How does hydrogen emit?When transitions from higher energy levels to the n = 1 energy level occur in a hydrogen atom, a range of electromagnetic radiation is emitted. This emission includes ultraviolet, visible, and infrared radiation.
The specific wavelength or frequency of the emitted radiation depends on the energy difference between the initial and final energy levels of the transition. Transitions from higher energy levels to the n = 1 energy level correspond to higher energy differences, resulting in the emission of shorter wavelength ultraviolet radiation.
As the energy differences decrease, the emitted radiation shifts towards longer wavelengths, covering the visible spectrum and extending into the infrared region.
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what is the thinnest soap film (excluding the case of zero thickness) that appears black when viewed by reflected light with a wavelength of 460 nm ? the index of refraction of the film is 1.33, and there is air on both sides of the film.
The thinnest soap film that appears black when viewed by reflected light with a wavelength of 460 nm is approximately λ/4n, where λ is the wavelength of light and n is the refractive index of the film.
When light reflects off a soap film, interference occurs between the reflected waves from the top and bottom surfaces of the film. For constructive interference to happen, the path length difference between the two waves must be an integer multiple of the wavelength. In the case of a film that appears black, we are interested in the condition where the path length difference is half a wavelength (λ/2).
For a soap film with air on both sides, the effective path length difference is twice the thickness of the film. Therefore, we want the thickness of the film to be approximately λ/4 in order to achieve the desired λ/2 path length difference.
Using the given wavelength of 460 nm (or 460 x 10^(-9) meters) and the refractive index of the film (1.33), we can calculate the thinnest soap film thickness by dividing λ/4 by the refractive index:
Thinnest film thickness = (λ/4) / n = (460 x 10^(-9) m / 4) / 1.33
After performing the calculations, we find that the thinnest soap film that appears black when viewed by reflected light with a wavelength of 460 nm is approximately 86.47 nm.
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a 44.1-cm-long wire with a mass of 13.9 g is under a tension of 48.7 n. both ends of the wire are held rigidly while it is plucked. a) what is the speed of the waves on the wire?
The speed of the waves on the a 44.1-cm-long wire is 38.2 m/s.
The speed of a wave indicates how fast a disturbance propagates through a medium or space. It is the speed at which the energy of the wave propagates through the medium or space. The speed of a wave depends on the properties of the medium or space through which it travels such as density, elasticity and temperature.
speed of the waves= v = √(T/μ)
where v = speed of the waves
T = tension in the wire
μ = linear mass density of the wire.
μ = m/L
where m = mass of the wire
L = length
μ = m/L = 0.0139 kg / 0.441 m
μ = 0.0315 kg/m
Therefore, v = √(T/μ) = √(48.7 N / 0.0315 kg/m) ≈ 38.2 m/s
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Which of the following factors has no effect on the force of friction between two solid objects? A.the type of materials the objects are made of. B.the smoothness of the surfaces between the objects. C.the contact force between the objects. D.the relative speed of the objects to each other
The required correct answer is A - the type of materials the objects are made of.
The force of friction between two solid objects depends on various factors such as the smoothness of the surfaces in contact, the contact force between the objects, and the relative speed of the objects to each other. The force of friction arises due to the interlocking of surface irregularities between two solid objects in contact, which resists the relative motion between them. The smoother the surfaces, the less force is required to overcome the friction. Similarly, the force of friction increases with the contact force between the objects and the relative speed of the objects to each other. However, the type of materials the objects are made of does not affect the force of friction, as long as they are both solid and in contact. Thus, the force of friction is an important concept in physics, which has numerous applications in daily life.
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a mixture containing 9 mol of f2 and 4 mol s is allowed to react. how many moles of f2 remain after 3 mol of s have reacted?
To determine the number of moles of F2 remaining after 3 mol of S have reacted, we need to consider the balanced chemical equation for the reaction between F2 and S. However, as the equation is not provided, we cannot provide an exact answer.
Assuming a simple stoichiometric ratio, let's consider the balanced equation:
F2 + S -> SF2
Based on this equation, for every 1 mol of S, 1 mol of F2 is required to react. Therefore, if 3 mol of S have reacted, we would expect 3 mol of F2 to have also reacted, assuming the reaction has gone to completion.
Since the initial mixture contained 9 mol of F2, and 3 mol of F2 have reacted along with the 3 mol of S, the remaining number of moles of F2 would be 9 - 3 = 6 mol.
Again, it's important to note that this is a simplified assumption based on a stoichiometric ratio, and the actual balanced equation may differ, which would affect the final result.
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when you take a snapshot of a standing wave in a string a quarter period in, the string is flat everywhere. what happened to the energy of the wave?
Answer:
The energy got changed to kinetic energy.
Explanation:
have a great day and thx for your inquiry :)
a standing wave is oscillating at 700 hz on a string, as shown in the figure. what is the speed of traveling waves on this string?
If a standing wave is oscillating at 700 hz on a string of wavelength 60cm, then the speed of traveling waves on the string is 420 m/s. The correct answer is C.
Wavelength is the distance between two corresponding points on a wave, such as the distance between two consecutive crests or troughs. It is a fundamental property of waves that determines their size or spatial extent.
To determine the speed of traveling waves on the string, we need to use the equation:
v = f * λ
where v is the speed of the waves, f is the frequency, and λ is the wavelength.
In this case, the frequency is given as 700 Hz, and the wavelength is given as 60 cm (0.6 m).
Plugging in the values:
v = 700 Hz * 0.6 m
v = 420 m/s
Therefore, the speed of traveling waves on the string is 420 m/s.
The question is incomplete I think the question is,
A standing wave is oscillating at 700 Hz on a string, as shown in the figure. What is the speed of traveling waves on this string? 60 cm wave
A. 140 m/s
B. 290 m/s
C. 420 m/s
D. 220 m/s
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based on the diagram, which processes would provide the energy used to generate electricity at the power plant?responsesabsorption of incoming solar radiationabsorption of incoming solar radiationfusion of atomic nuclei to form heavier nucleifusion of atomic nuclei to form heavier nucleicombustion of fossil fuelscombustion of fossil fuelsfission in radioactive fuel
combustion of fossil fuels would provide the energy used to generate electricity at the power plant.
What is a coal-fired power plant?Thermal power plants relying on coal for their operations are identified as coal fired power plants.
Coals formation results from the accumulation and transformation over millions of years under high temperatures and pressures through underground vegetation decomposition processes making it a fossil fuel resource. Upon combustion significant amounts of heat energy are released enabling its conversion into electricity production purposes.
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an electric heater is really just a resistor with a voltage across it. if you want to have 530 w of heat with a voltage v = 125 volts, what resistance (ω) should the heater coil have?
The resistance (ω) that the heater coil should have to produce 530 W of heat with a voltage v = 125 volts is 29.5 ohms.
The formula to calculate power (P) in an electric circuit is
P = V²/R,
where V is the voltage and R is the resistance of the circuit.
In this case, we have the power (P) of 530 W and the voltage (V) of 125 volts. We need to find the resistance (R) of the heater coil.
We can rearrange the formula as R = V²/P to solve for the resistance.
Substituting the values,
we get R = 125²/530, which equals 29.5 ohms.
An electric heater works on the principle of converting electrical energy into heat energy. The heater coil in the heater acts as a resistor, which impedes the flow of current and causes electrical energy to be converted into heat. The amount of heat produced by the heater depends on the power rating of the heater and the voltage applied to it.
It is important to note that the resistance of the heater coil determines the amount of current that flows through it, which in turn affects the amount of heat produced by the heater. If the resistance is too high, the current flow will be low, and the heater will not produce enough heat. If the resistance is too low, the current flow will be high, and the heater may overheat and become a fire hazard. Therefore, it is important to choose the correct resistance for the heater coil to ensure safe and efficient operation.
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A bottle has a mass of 35.0g when empty and 98.44g when filled with water. When filled with another fluid, the mass is 88.78g. what is the specific gravity of this other fluid?
The specific gravity of the other fluid is 2.43, When filled with another fluid, the mass is 88.78g.
The specific gravity of a substance is the ratio of its density to the density of water. In this case, we can use the masses of the empty bottle, the bottle filled with water, and the bottle filled with the other fluid to calculate the specific gravity of the other fluid.
First, we need to calculate the mass of the water in the bottle, which is the difference between the mass of the filled bottle and the mass of the empty bottle:
mass of water = 98.44g - 35.0g = 63.44g
Next, we can use the mass of the water and the density of water (1.00 g/mL) to calculate the volume of the water:
volume of water = mass of water / density of water = 63.44g / 1.00 g/mL = 63.44 mL
Now, we can use the mass of the bottle filled with the other fluid and the volume of the water to calculate the density of the other fluid:
mass of other fluid = 88.78g
volume of other fluid = volume of bottle - volume of water = 100mL - 63.44mL = 36.56 mL
density of other fluid = mass of other fluid / volume of other fluid = 88.78g / 36.56 mL = 2.43 g/mL
Finally, we can calculate the specific gravity of the other fluid by dividing its density by the density of water:
specific gravity = density of other fluid / density of water = 2.43 g/mL / 1.00 g/mL = 2.43
Therefore, the specific gravity of the other fluid is 2.43.
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find the velocity v(t) and speed ∥v(t)∥ of a particle whose motion is described by x=5,y=t2−4t 4,z=2t3−6t2
if two objects have different inertia, then one of the objects is necessarily larger than the other. true .false
Answer:
True
Explanation:
The more inertia that an object has, the more mass that it has.
Which of the following is required to have a backfire flame arrestor?
Flares are rated for day, night or combined day/night use.
VHF radios work by the line of sight principle.
A boat with a gasoline inboard engine.
A boat with a gasoline inboard engine requires a backfire flame arrestor.
This safety device is designed to prevent the occurrence of a backfire in the engine compartment, which could lead to a dangerous fire or explosion. The backfire flame arrestor is typically installed in the air intake system of the engine and is responsible for trapping and extinguishing any flames or sparks that may be generated during the engine operation.
By doing so, it helps to prevent the ignition of fuel vapors in the engine compartment. It is an essential component for the safe operation of gasoline-powered inboard engines, ensuring the protection of the vessel and its occupants from potential hazards associated with backfires.
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because of the properties of degenerate matter, white dwarfs follow a mass-radius relationship___________________________________________,
Because of the properties of degenerate matter, white dwarfs follow a mass-radius relationship known as the Chandrasekhar limit.
The mass-radius relationship for white dwarfs is an inverse relationship due to the properties of degenerate matter. This means that as the mass of a white dwarf increases, its radius decreases, making the star more compact and dense. This unique behavior is a result of electron degeneracy pressure, which counteracts the force of gravity in these compact stellar remnants. This relationship dictates that as the mass of a white dwarf increases Sun and planets, its radius decreases. This is due to the increasing gravitational force compressing the degenerate matter to a smaller volume. The Chandrasekhar limit also sets the maximum possible mass for a white dwarf, at around 1.4 times the mass of our sun, beyond which the white dwarf will collapse and potentially form a supernova or neutron star.
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A projectile is fired with an initial speed of 150 m/s at an angle of 47 degrees above the horizontal. Determine the velocity of the projectile 2seconds after firing. Determine the total time in the air. Determine the maximum height reached by the projectile.
The maximum height reached by the projectile is approximately 283.13 meters.
To determine the velocity of the projectile 2 seconds after firing, we need to break down the initial velocity into its horizontal and vertical components.
The horizontal component remains constant throughout the motion, so it will be the same as the initial velocity: 150 m/s.
For the vertical component, we can use the equation v = u + at, where v is the final velocity, u is the initial vertical velocity component, a is the acceleration due to gravity (-9.8 m/s^2), and t is the time.
Since the projectile is fired upwards, the initial vertical velocity component is given by u = u_initial * sin(angle), where u_initial is the initial velocity (150 m/s) and the angle is 47 degrees.
Using this information, we can calculate the vertical velocity component at t = 2 seconds:
v = u + at
v = (u_initial * sin(angle)) + (a * t)
v = (150 * sin(47)) + (-9.8 * 2)
v ≈ 76.65 - 19.6
v ≈ 57.05 m/s
So, the velocity of the projectile 2 seconds after firing is approximately 57.05 m/s.
To determine the total time in the air, we need to find when the projectile returns to the same height from which it was launched. The total time in the air can be calculated using the equation t = (v_final - u_initial * sin(angle)) / (-a), where v_final is the final vertical velocity component (0 m/s).
0 = (u_initial * sin(angle)) + (-9.8 * t_total)
t_total = (u_initial * sin(angle)) / 9.8
Using the given values, the total time in the air is approximately:
t_total = (150 * sin(47)) / 9.8
t_total ≈ 6.42 seconds
So, the total time in the air is approximately 6.42 seconds.
To determine the maximum height reached by the projectile, we can use the equation h_max = (u_initial^2 * sin^2(angle)) / (2 * a), where h_max is the maximum height.
h_max = (150^2 * sin^2(47)) / (2 * 9.8)
h_max ≈ 283.13 meters
Therefore, the maximum height reached by the projectile is approximately 283.13 meters.
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A 0.15 kg baseball traveling horizontally is hit by a bat and its direction exactly reversed. Its velocity changes from +20m/s to -20 m/s.a. What is the magnitude of the impulse delivered by the bat to the ball?b. If the baseball is in contact with the bat for 1.3 ms, what is the average force exerted by the bat on the ball?
The magnitude of the impulse delivered by the bat to the ball is 6.0 Ns. The average force exerted by the bat on the ball is 4.6 x 10^3 N.
Given: mass of baseball m = 0.15 kg, initial velocity u = +20 m/s, final velocity v = -20 m/s, time of contact t = 1.3 ms = 0.0013 s
To find the magnitude of impulse delivered by the bat to the ball, we can use the impulse-momentum theorem:
Impulse = Change in momentum
Impulse = m(v - u)
Impulse = 0.15(-20 - 20)
Impulse = -6 Ns (the negative sign indicates that the impulse is in the opposite direction to the initial velocity)
Therefore, the magnitude of the impulse delivered by the bat to the ball is 6 Ns.
To find the average force exerted by the bat on the ball, we can use the definition of average force:
Average force = Impulse / time of contact
Average force = -6 / 0.0013
Average force = -4,615.38 N (the negative sign indicates that the force is in the opposite direction to the initial velocity)
Therefore, the average force exerted by the bat on the ball is 4,615.38 N.
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