The magnitude of the charge on the particle is 0.0083 C.
Solution:
The centripetal force if it is moving in a circle is mv^2/r. Since this is coming from the magnetic force, then
mv^2/r = qvB
q = (mv^2/r)/(vB) = (mv)/(rB)
q = .002*5/(.2*6) = 0.0083 C
The magnitude of the electric field E produced by a charged particle at a point P is the electric force per unit positive charge exerted on another charged particle at that point. The direction of the electric field is the direction of the force on the positive charge. The electric field vector magnitude is calculated as the force per charge for any testing charge in the electric field.
The force on the test charge can be directed toward the source charge or directly away from the source charge. Electron charge can be determined simply by placing a known number of electrons on one electrode of a capacitor and measuring the voltage Vs across the capacitor.
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an object has mass 0.2 kg, how much force is required to throw it vertically with velocity 5ms
0.2×51000)
Explanation:
change 5ms into cms before multiplying by 0/2 kgs
A skier (m = 100 kg) is on level ground with a coefficient of kinetic friction of 0.05 m
moving at a speed of 100m/s. Calculate the distance the skier will go before they stop.
Use conservation of energy.
The distance the skier will go before they stop is 10193.68m.
Given ; Mass =100kg
coefficient of kinetic friction μ=0.05m
u=100m/s
v=0
μg=a
a= μg=0.05 x 9.81=0.4905 m/s²
v²-u²=2as
[v²-u²]/2a= s
-100²/2(0.4905)
s=10193.68m (neglecting the negative sign)
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Vector A is 3.2 m in length and points along the positive y-axis. Vector B is 4.6 m in length and points
along a direction 195° counterclockwise from the positive x-axis. What is the magnitude of the resultant
when vectors A and B are added?
a bus traveled 387 km in 5 h.one hour of the trip was in city traffic. the bus's city speed was just half of its speed on open highway. the rest of the trip was on open highway. find the bus'scity speed
The bus'scity speed is 77.4km/hr.
How is speed defined in?What constitutes speed? the speed of a change in an object's position in any direction.
Speed is the rate of change in location of an item, expressed in meters per second. If something starts at the origin and goes three meters in three seconds, for instance, its speed is one meter per second. Like distance divided by time, the equation for speed is straightforward.
A change in an object's position over time is referred to as motion in physics. Displacement, distance, velocity, acceleration, time, and speed all play a role in how motion is defined. Speed is a scalar variable that describes how quickly an object travels through space with regard to time.
speed = distance/time
speed =387/5
speed =77.4km/hr.
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A 65-kg diver jumps off a 9.7-m tower.
(a) Find the diver's velocity when he hits the water.
____m/s
(b) The diver comes to a stop 2.0 m below the surface. Find the net force exerted on the diver while in the water.
______N
(a) The diver's velocity when he hits the water is 13.795 m/s.
(b) The diver's net force while in the water was -3092.7N.
Newton's second law states that the force F acting on a body is equal to the mass m of the body multiplied by the acceleration an of its center of mass, F = ma.
The three equations of motion are: v = u + at, v2 = u2 + 2as, and s = ut + 12at2.
Given
A 65-kg diver jumps off a 9.7-m tower
(a) Using newton's equation of motion,
v² = u² + 2gs ......... (1)
Where v = final velocity,
u = initial velocity,
s = height of the tower,
g = acceleration due to gravity.
Given: s = 9.7 m, u = 0 m/s (height jump), g = 9.81 m/s2.
Substitute into equation 1
v² = 0² + 2×9.81×9.7
v² = 190.314
v = √(190.314)
v = 13.795 m/s.
As a result, the driver's velocity when he hits the water is 13.795 m/s.
(b)
F = ma. ......... (2)
Where F is the force applied to the diver, m is the diver's mass, and an is the diver's acceleration below the water's surface.
Also using
v² = u² + 2as ......... (3)
When the diver enters the water, u = 13.795 m/s, and when the diver comes to a complete stop, v = 0 m/s.
Given are the following values: s = 2.0 m, u = 13.795 m/s, and v = 0 m/s.
Substitute in equation 3
0² = 13.795²+2(2a)
0 = 190.30203 + 4a
-4a = 190.30203
a = 190.30203/-4
a = -47.58 m/s²
Also given: m = 65 kg,
Substitute into equation 3
F = (-47.58)(65)
F = -3092.7
The Force is negative because it acts against the diver's motion.
As a result, the net force exerted on the diver while in the water equals -3092.7N.
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what is the wavelength (in pm) of an electron with a mass of 9.11 x 10-31 kg and a velocity of 2.963 x 106 m/s aleks
The wavelength of an electron is 215.5nm.
The de Broglie wavelength is calculated in what way?A description of the de Broglie wavelength is as follows:
The formula for wavelength is = h/mv, where h stands for Planck's constant, m for mass, and v for velocity.
The equation p = h/λ, where h is the Planck constant and is the wavelength, expresses the De Broglie relation, which states that there is a correlation between an electron's wavelength and momentum.
The wavelength of a wave is the distance between its two subsequent crests or troughs.
h = 6.62607015 × 10⁻³⁴ joule second.
m =9.11 x 10 ⁻³¹Kg
v = 2.963 x 10⁶m/s
λ = h / ( mv)
λ = 6.62607015 × 10⁻³⁴/9.11 x 10 ⁻³¹×2.963 x 10⁶
λ = 2.155×10⁻⁷
λ = 215.5nm.
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when the core of a star reaches a temperature of about 100 million degrees (k), something new happens in the core. what is this new event?
When the core of a star reaches a temperature of about 100 million degrees (k), the new event named triple-alpha process happens where the helium will begin to fuse into carbon.
What is triple alpha process?The triple-alpha mechanism, which turns three helium nuclei into one carbon atom, will start to fuse helium into carbon when the temperature in the core reaches roughly 100 million degrees. There is a lot of heat produced by this.
The triple-alpha process is unusually sensitive to temperature; when the reaction's temperature is doubled, it proceeds nearly a trillion times faster! Therefore, while the fusing helium heats the core, which cannot expand to cool down, the increasing temperature prompts the helium fusion to abruptly proceed millions of times faster, which very quickly heats the core even more, which in turn prompts the helium to fuse way, way faster.
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what is the magnification of an astronomical telescope whose objective lens has a focal length of 79 cm and whose eyepiece has a focal length of 2.9 cm ? follow the sign conventions.
The magnification of an astronomical telescope is -27.24 .
The magnification of a telescope is actually a relationship between two independent optical systems: the telescope itself and the eyepiece that is being used.
To determine the power, divide the focal length of the telescope (in mm) by the focal length of the eyepiece (in mm)Magnification is denoted by MMathematically it is M = -(T/E)Focal length of the telescope = T = 79 cm = 790mm
Focal length of the eyepiece = E = 2.9 cm = 29mm
M = -[tex]\frac{T}{E}[/tex]
M = -[tex]\frac{79}{2.9}[/tex]
M = -27.24
Therefore, the magnification of an astronomical telescope is -27.24.
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a bear sling is used in some national parks for placing backpackers' food out of the reach of bears. as the backpacker raises the pack by pulling down on the rope, the force f needed:
Force is to be known for this problem.
What is force?
In physics, force is the push or pull that an object feels when its mass causes it to change its velocity. An external force has the ability to change a body's resting or moving state. It moves and has a size.
What constitutes speed?
the speed at which the position of an object is shifting, in any direction. Speed is defined as the product of the distance traveled and the time needed to cover that distance. Since speed simply has a focus and no magnitude, it is a scalar number.
2T cos∅ =μg
⇒ if weight (μg)
rises
⇒∅ increases
⇒ cos∅ decreases
⇒T increases
⇒F will also increases
But ∴ Cos 90° = u
⇒ not possible.
Therefore, the force is to be needed.
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many astronomers believe that the massive object at the center of the milky way galaxy is a black hole. if so, what must the schwarzschild radius rs of this black hole be?
The Schwarzschild Radius Rs of this black hole is 5.69 x [tex]10^{10}[/tex] m
The Schwarzschild radius or gravitational radius is a physical parameter in the Schwarzschild solution of Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole.
Let's assume that the ring shaped disk is circular and thus, to find the mass of the object at the center of the milky way, we can use the circular orbit equation;
v = √(GM/r)
where;
G is the gravitational constant and has a value of 6.67 x 10^(-11) Nm²/kg²
R is the radius of the orbit,
M is the mass of the larger object
v = velocity = 190km/s = 190000 m/s
Also
1 light year = 9.4605 x 10^(15) m
Thus,7.5 light years = 7.5 x 9.4605 x 10^(15) m
so, M = v²r/G
Putting all the values in the equation,
M = [190000² x 7.5 x 9.4605 x 10^(15)]/6.67 x 10^(-11)
M = 3.84 x 10^(37) kg
Now, mass of the sun generally has a value of 1.9891 x 10^(30) kg
Thus, value of mass of object in solar masses = 3.84 x 10^(37)/1.9891 x 10^(30) = 1.931 x 10^(7) solar masses
The formula for Schwarzschild radius is given as;
Rs = 2GM/c²
Where c is speed of light = 3 x 10^(8) m/s
Thus,
Rs = 2 x 6.67 x 10^(-11) x 3.84 x 10^(37)/(3 x 10^(8))² = 5.69 x [tex]10^{10}[/tex] m
The Schwarzschild radius Rs of this black hole is 5.69 x [tex]10^{10}[/tex] m
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x. a 0.015-kg marble moving to the right at 0.40 m/s has a head-on, elastic collision with a 0.045-kg marble sitting at rest on a smooth, level surface. a) what are the magnitudes and directions of the velocities of the two marbles after the collision? b) show that the ke is conserved.
The magnitudes and directions of the velocities of the two marbles after the collision is: v1f is left and v2f is right.
What is collision?The initial marble weighs m1 = 0.015 kg.
Second marble's mass is m2=0.045kg.
The first marble's initial velocity is v1i=0.40m/8 before to contact.
The second marble's initial velocity is v2i=0m/8 prior to impact.
After the impact, the first marble's final speed is v1f.
Following the collision, the initial marble's final velocity is v2f.
If the collision is elastic, the kinetic energy is preserved.
We'll write 1/2 m1 for KE = 1/2 mv2 (v1i)
2 + 1/2 m2(vi) (vi)
2 = 1/2 m1(v1f)2 + 1/2 m2 (v2f) (v2f)
2.
Using this equation, we can establish a new relationship between velocities and determine each marble's post-collision velocity:
v1f=(m1-m2)/(m1+m2)
v1\sv1f=(0.015kg-0.045kg)/(0.015kg+0.045kg)
0.40m/s\s=-0.20m/s
First marble is moving leftward at 0.20 m/s, as indicated by the negative sign.
Find the second marble's final velocity.
v2f=2m1v1/(m1+m2)\s
v2f=2⋅0.015kg⋅0.40m/s/(0.015kg+0.045kg)\s
v2f=0.20
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an electron is released within a uniform electric field of a magnitude of 28,000 n/c generated by two parallel plates. the plates are separated by 4 cm. if the electron has moved across the entire gap between the plates, what is its speed?
Within a uniform electric field of magnitude 28,000 n/c produced by two parallel plates, an electron is expelled at a speed of 3.51 * 10^15 m/s^2. The distance between the plates is 4 cm.
The electron is a subatomic particle with the symbol e or with an electric field of one elementary negative charge. Due to their lack of known components or substructure, electrons, which are part of the first generation of the lepton particle family, are typically considered to be elementary particles. When the electric field strength at the electron's location, E, is taken into account, the force acting on it has the size F=eE. Newton's second law provides the electron's acceleration as follows:
a= F/m = eE/m
= (1.60*10^-19)(2.00*10^4)/9.11*10^-31
= 3.51 *10^15 m/s^2
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An astronaut orbits the Earth in a space station.Which is a vector quantity
The force of gravity is the only force acting upon their body. The astronauts are in free-fall.
If the astronaut is formed of the same amount of material as before, the mass will always be the same.
So, when asked what the astronauts' mass is on the space station, we can respond it's still 65 kg. Because there is no gravity in space, astronauts float around.
Everyone understands that the gravitational force decreases with distance from Earth. Astronauts are so far away from Earth that gravity is negligible. This is why NASA refers to it as microgravity.
Mass is the same whether measured on Earth or on the International Space Station. Weight can vary based on gravitational pull, such as on the Moon, where weight is one-sixth that of Earth.
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Calculate the efficiency of a machine that requires 20 J of input work to do 10 J of output work. What is the efficiency of the machine? (in percent, but write the number only)
The efficiency of a machine that requires 20 J of input work to do 10 J of output work. The efficiency of the machine η = 50 %
The engine efficiency is defined as ratio of the useful work done to the heat provided.
By using the formula for efficiency of a machine and substituting the values in it, we get :
η = (Wo/Wi × 100)%
η = (10/20 × 100)%
η = 50 %
The efficiency of the machine will be η = 50 %
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An aeroplane lands on a runway at a speed of 180 km/hr and is brought uniformly in 30 seconds.what distance does it covers on the run way before coming to rest
This can be calculated by using motion equations, The distance covered on the runway before coming to rest
Initial speed is 180 km/hr = 50 m/s
time took to come to rest is = 30 sec
so we can write, here we are assuming that there is no frictional force is applied externally or internally to the system.
u = 50 m/s
v = 0 m/s
t = 30 s
we know that distance travelled = x
so, x =
putting the appropriate values, we get that
x = [tex](\frac{50+0}{2} ) 30[/tex]
x = 750 m
Hence the distance travelled before coming to rest is 750 m.
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the tide that results from a lunar wave is larger than the solar wave. group of answer choices true false
The given statement is true. A lunar eclipse happens when the Moon passes into the shadow of the Earth. A solar eclipse happens when the Moon passes between Earth and the Sun.
What is lunar wave and solar wave?A lunar eclipse happens when the Moon passes into the shadow of the Earth. This is only possible when the Sun, Earth, and Moon are precisely or extremely closely aligned with Earth between the other two, which can happen only on a full moon night when the Moon is close to either lunar node.
A solar eclipse happens when the Moon passes between Earth and the Sun, completely or partially blocking Earth's view of the Sun. A new moon corresponds with such an alignment, showing that the Moon is closest to the plane of the Earth's orbit. The Moon completely obscures the disk of the Sun during a total eclipse.
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The given statement is true. A lunar eclipse happens when the Moon passes into the shadow of the Earth. A solar eclipse happens when the Moon passes between Earth and the Sun.
What is lunar wave and solar wave?When the Moon enters the shadow of the Earth, an eclipse occurs. This can only occur on a full moon night when the Moon is close to either lunar node, when the Sun, Earth, and Moon are precisely or extremely closely aligned with Earth between the other two.When the Moon passes in front of Earth and the Sun, covering Earth's view of the Sun entirely or in part, a solar eclipse occurs. Such an alignment is accompanied by a new moon, demonstrating that the Moon is closest to the plane of the Earth's orbit. A total eclipse occurs when the Moon totally blocks out the Sun's disk.To learn more about Lunar and solar eclipse refer to:
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(b) The cars collide and car B experiences an impulse. Car A continues to move in the same
direction, with a momentum of 21 000 kg m/s.
(i) Calculate the momentum of car B immediately after the collision.
momentum =
llicion
[1]
The momentum of car B immediately after the collision if the momentum of car A is 21 000 kg m/s after collision is 15000 kg m / s
p = m v
p = Momentum
m = Mass
v = Velocity
m1 = 2000 kg
u1 = 18 m / s
pi1 = 2000 * 18
pi1 = 36000 kg m / s
m2 = 1200 kg
u2 = 0
pi2 = 0
pf1 = 21000
According to law of conservation of momentum
pi1 + pi2 = pf1 + pf2
pi1 = Initial momentum of car A
pi2 = Initial momentum of car B
pf1 = Final momentum of car A
pf2 = Final momentum of car B
pf2 = pi1 + pi2 - pf1
pf2 = 36000 + 0 - 21000
pf2 = 15000 kg m / s
Therefore, the momentum of car B immediately after the collision is 15000 kg m / s
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a 500-w device is connected to a 120-v ac power source. what is the peak voltage across this device? a) 4.2 v b) 5.9 v c) 120 v d) 150 a e) 170 v
The peak voltage across this device would be 170v (rounded). So the answer is E.
What is peak voltage?It is the highest point or highest value of voltage for any voltage waveform. It is a power quality issue that occurs when devices that use Pulse Width Modulation, such as a variable frequency drive, is added to a power system. The resulting peak voltage is a result of the switching speed and length of cable (increasing impedance).
Now, we need to find the peak voltage based on the information given from the question.
Vrms = 120V (given)
the formula is Vrms = Vpeak / [tex]\sqrt{2}[/tex]
Vpeak = [tex]\sqrt{2[/tex]Vrms
= [tex]\sqrt{2}[/tex] * 120
Vpeak = 170v (rounded)
So, the peak voltage of this device would be (E) 170v.
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A 0. 25-kg toy car experiences a net force of 9. 0 n while slowing down to a complete stop. What is the magnitude of its acceleration?.
Answer:
a = 36 m/s
Explanation:
Given:
F = 9 N
m = 0.25 kg
a= ?
Use the equation:
F = ma (divide by m on both sides to get a alone)
a = F/m= 9/0.25 = 36 m/s
robin started at point a. she walked 4m south, then 8m east, then 4m north, then 8m west so that she was back at point a. if her walk took 5 minutes, what was her velocity in meters per minute?
Robin started at point a. she walked 4m south, then 8m east, then 4m north, then 8m west so that she was back at point a. if her walk took 5 minutes her velocity in meters per minute is 0.96.
Displacement = distance / time = 24m/5 = 4.8
Velocity = displacement / Time = 4.8/5 = 0.96m/min
Its scientific definition and velocity are presumably similar. You are aware that a significant displacement over a short period of time indicates a large velocity, and that velocity has measures of distance / time, like miles/hour or kilometers/hour.
The change in position divided by the distance travelled is the definition of average velocity. However, the average speed of an object tells us nothing about what happens to it between the starting and finishing points. For instance, average velocity does not allow us to determine whether a passenger in an airplane briefly stops or reverses before relocating to the rear of the aircraft. We must consider shorter distances travelled over shorter times in order to obtain more information.
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the frequency content of an analog signal to be digitized has a range roughly covering the range of the auditory system of a young child: 200 hz to 20,000 hz. for accurate sampling, what is the minimal sampling rate necessary for an a/d convertor?
For accurate sampling, -44.1khz is minimum sampling rate for an a/d convertor.
What is sampling rate?The number of samples per second (or other unit) taken from a continuous signal to form a discrete or digital signal. The sample rate or sample rate specifies the number of samples per second (or other unit). of a continuous signal to form a discrete or digital signal..
The sampling rate can be thought of as the audio version of frames per second. This is the number of "clips" taken from an analogue sound wave to make a digital file. In addition, the sample rate also controls the highest frequency that can be accurately reproduced by a digital file.
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a car traveling with a constant velocity quickly comes to rest. while slowing down, the passengers inside the car are pushed forward by the force of .
Using the concepts of motion, we got that Ma is the force exerted on the passengers inside the car when a car traveling with a constant velocity quickly comes to rest.
We know very well that according to newton second law of motion,
if a moving object is moving with some velocity v at any particular time t, then there is force acting on that object and that force is given by
F= dp /dt,
where dp is defines as change in momentum of the object. In other words,
dp=M×([tex]v_f_i_n_a_l[/tex] - [tex]v_i_n_i_t_i_a_l[/tex])
where [tex]v_f_i_n_a_l[/tex] and v[tex]_i_n_i_t_i_a_l[/tex] are the velocities of the object in different time.
So suppose car has some mass M kg
It is given that final velocity of the object is =0 as the car comes to rest,
suppose initial velocity is v
Therefore, F=[M×(0-v)]/t
=> F= -M×(v/t)
=> F= -Ma because acceleration =velocity/time
Here negative sign shows that force acts on the person in opposite direction of frictional force applied by the road.
Hence, when a car traveling with a constant velocity quickly comes to rest. while slowing down, the passengers inside the car are pushed forward by the force - Ma.
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two 16.0 $kg$ ice sleds are placed a short distance apart, one directly behind the other, as shown in the figure. a 3.11 $kg$ cat, initially standing on sled 1, jumps across to sled 2 and then jumps back to sled 1. both jumps are made at a horizontal speed of 2.00 $m/s$ relative to the ice. what is the final speed of sled 2? (assume the ice is frictionless.)
The final speed of sled 2 = 0.77 m/s
What is impulse?Impulse is the integral of the force (F) over the time interval (t) for which the force acts. Since force is a vector quantity, momentum is also a vector quantity. Momentum applied to an object produces a vector change equivalent to its linear momentum, and the resulting direction is also changed.
For the given case:
After first jump speed of sled 1 is = u₁
Since there is no external force acting on the sled-cat system there'll be no change in momentum.
u₁ × 16 + 2 × 3.11 = 0
u₁ = -0.38 m/s
Now, for sled 2
2 × 3.11 = (3.11 + 16)u₂
u₂ = 0.32 m/s
After the second jump:
-2 × 3.11 + 16 × v₂ = 0.32 × (16 + 3.11)
v₂ = 0.77 m/s
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what is the rotational inertia of a solid iron disk of mass 41.0 kg with a thickness of 5.00 cm and radius of 30.0 cm, about an axis perpendicular to the disk and passing through its center?
Answer:
I = 1/2 M R^2 moment of inertia of solid disk
I = 1/2 * 41.0 kg * (.3 m)^2
I = 20.5 kg * .09 m^2 = 1.85 kg-m^2
a satellite moves on a circular earth orbit that has a radius of 6.7 x 106 m. a model airplane is flying on a 15-m guideline in a horizaontal circle. the guideline is parallel to the ground. find the speed of the plane such that the plane and the satellite have the same centripetal acceleration.
The speed of the plane will have a factor of 0.668 with the satellite speed at the same centripetal acceleration.
We need to know about centripetal acceleration to solve this problem. The centripetal acceleration depends on the angular velocity and the radius. It can be written as
a = v² / R
where a is centripetal acceleration, v is velocity and R is radius.
From the question above, the given parameters are
R1 = 6.7 x 10⁶ m
R2 = 15 m
a1 = a2
By substituting the given parameters, we can calculate the speed of plane
a1 = a2
v1² / R1 = v2² / R2
v2² / v1² = R1 / R2
v2² / v1² = 6.7 x 10⁶ / 15
v2² / v1² = 6.7 x 10⁶ / 15
v2/v1 = 0.668
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If the man pulls the sled with a 10 N
force, what is the horizontal component
of force? Refer to chapter 4, mechanics if
you do not remember how to resolve a
force into its components.
Answer:
Explanation:
The horizontal component of force is Fcosθ if the man pulls the sled with a 10 N force. Force has both a magnitude and a direction since it is a vector quantity.
What is force?A force is an external cause that, when applied, alters or has the potential to alter a body's condition. The body comes to rest while it is moving, and it moves when it is at rest.
The body's orientation, form, size, etc. may also alter as a result. An illustration would be to push or forcefully shove a door. Force has both a magnitude and a direction since it is a vector quantity. If the man pulls the sled with a 10 N force then the horizontal component of force is Fcosθ. Your training at this level should place a major emphasis on the idea that a push or even a pull was referred to as an force.
Therefore, the horizontal component of force is Fcosθ if If the man pulls the sled with a 10 N force.
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explain the differences between linear speed and angular speed when describing motion along a circular path.
The difference between linear speed and angular speed is linear speed calculates the distance to time whereas angular speed calculates the angle to time.
The difference between the linear speed and the angular speed is that linear speed is just a measurement determined by calculating the distance of an arc versus time taken, and angular velocity is also a measurement determined by calculating the angle of an arc versus time taken.
The formula of the linear speed is
s = d / t
where s is the speed
d is the distance
t is the time taken
The formula of the angular speed is
ω = θ / t
where ω is the angular speed
θ is the angular rotation
t is the time taken.
The relation between the linear speed and angular speed in a uniform circular motion is
s = rω
where s is the linear speed
r is the radius
ω is the angular speed.
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2. It takes 1,200 J of work to lift a car high enough to change a tire.
How much work must be done by the person operating the jack
if the jack is 25% efficient?
The work done by the person operating the jack is 4,800 J
Efficiency is described as the potential to perform something with the least quantity of wasted time, cash, and attempt or competency in performance. Effectiveness is described because the diploma to which some thing is successful in producing a preferred result; achievement.
calculation:-
work input = (1200 J)/(0.25)
= 4800 J.
There are numerous styles of performance, consisting of allocative and effective performance, technical efficiency, 'X' efficiency, dynamic performance and social efficiency.
The prime focus of performance is for customers to get the goods and offerings they want at the bottom possible resource price. Inside the have a look at of economics, the dreams of efficiency and equity are frequently in warfare with each other.
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a ball is kicked with an initial velocity of 23 m/s in the horizontal direction and 14 m/s in the vertical direction. (assume the ball is kicked from the ground. for each answer, enter a number.) (a) at what speed (in m/s) does the ball hit the ground? m/s (b) for how long (in s) does the ball remain in the air? s (c) what maximum height (in m) is attained by the ball?
The speed of the ball is 192m/s. The long of the ball is 2.85s.The height of the ball is 2.13m.
How to calculate speed?A)The speeds at these points are equal since the starting position and the point at which it touches the ground have the same elevation. Solving the product of the horizontal and vertical velocities yields the final speed. Which is
vf=√(V[tex]ox[/tex])²+(V[tex]oy[/tex])²
vf=√(23m/s)²+(14m/s)²
vf=192m/s
How to calculate long?B)Take into account the starting point and the highest point, respectively.
We are aware that the vertical velocity is zero at the highest point. Additionally, we are aware that the duration of the flight from start to finish is twice as long.
So, we'll apply the formula t=v[tex]f[/tex]-v[tex]o[/tex]/a
t=2(v[tex]top[/tex]-v[tex]o[/tex])/a
t=2(0m/s-14m/s)/-9.81m/s
t=2.85s
How to calculate height?C)Using the formula, the highest height that can be reached can be determined.(v[tex]f[/tex])²=(v[tex]0[/tex])²+2ay
This is how the maximum height is determined:
(v[tex]f)[/tex]²=(v[tex]0)[/tex]²+2ay
y[tex]max[/tex]=(v[tex]top[/tex])²-(v[tex]o[/tex])²÷2a
y[tex]max[/tex]=(0m/s)²-(14m/s)²÷2(-9.81m/s)²
=2.13m
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a playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.350 rev/s. what is its angular velocity (in rev/s) after a 15.0 kg child gets onto it by grabbing its outer edge? the child is initially at rest.
Angular velocity (in rev/s) after a 15.0 kg child gets onto it by grabbing its outer edge is 1.575 rad/s.
The angular velocity of the merry-go-round after a child gets on it is equal to the angular velocity of the child plus the angular velocity of the merry-go-round.
The angular velocity of a rotating object can be calculated using a formula:
ω = ω + (m/r)
where ω is the original angular velocity, m is the mass of an object that's been added to it, r is its radius, and (m/r) is the change in mass divided by its radius. When we plug in our values for this problem, we get:
ω = 0.350 rad/s + ((15 kg)/(1.8 m)) rad/s
= 0.350 rad/s + 1.25 rad/s
= 1.575 rad/s
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