Answer:
a) The initial speed of the projectile is approximately 42.410 meters per second.
b) The speed of the projectile after 4 seconds is approximately 21.352 meters per second.
c) The horizontal range of the projectile is 169.64 meters.
d) The maximum height of the projectile is 68.775 meters.
e) The speed of the projectile when it landed on the ground is approximately 46.807 meters per second.
Explanation:
According to the statement, the projects shows a parabolic motion, which consists in the combination of horizontal uniform motion and vertical uniformly accelerated motion due to gravity. This motion is represented by the following equations of motion:
[tex]x = x_{o} + v_{o}\cdot t\cdot \cos \theta[/tex] (1)
[tex]y = y_{o} + v_{o}\cdot t\cdot \sin \theta + \frac{1}{2}\cdot g\cdot t^{2}[/tex] (2)
Where:
[tex]x_{o}[/tex], [tex]x[/tex] - Initial and current horizontal position, measured in meters.
[tex]y_{o}[/tex], [tex]y[/tex] - Initial and current vertical position, measured in meters.
[tex]\theta[/tex] - Launch angle, measured in sexagesimal angle.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
[tex]t[/tex] - Time, measured in second.
a) By using (2) and knowing that [tex]y_{o} = 20\,m[/tex], [tex]y = 0\,m[/tex], [tex]t = 8\,s[/tex], [tex]\theta = 60^{\circ}[/tex] and [tex]g = -9.807\,\frac{m}{s^{2}}[/tex], then initial speed of the projectile is:
[tex]v_{o}\cdot t \cdot \sin \theta = y-y_{o}-\frac{1}{2}\cdot g\cdot t^{2}[/tex]
[tex]v_{o} = \frac{y-y_{o}-\frac{1}{2}\cdot g\cdot t^{2} }{t\cdot \sin \theta}[/tex]
[tex]v_{o} = \frac{0\,m-20\,m-\frac{1}{2}\cdot \left(-9.807\,\frac{m}{s^{2}} \right)\cdot (8\,s)^{2} }{(8\,s)\cdot \sin 60^{\circ}}[/tex]
[tex]v_{o} \approx 42.410\,\frac{m}{s}[/tex]
The initial speed of the projectile is approximately 42.410 meters per second.
b) The vertical component of the velocity of the projectile is determine by differentiating (2) in time and substitute all known values:
[tex]v_{y} = v_{o}\cdot \sin \theta +g\cdot t[/tex] (3)
([tex]v_{o} \approx 42.410\,\frac{m}{s}[/tex], [tex]\theta = 60^{\circ}[/tex], [tex]g = -9.807\,\frac{m}{s^{2}}[/tex] and [tex]t = 4\,s[/tex])
[tex]v_{y} = -2.5\,\frac{m}{s}[/tex]
The horizontal component of the velocity of the projectile is:
[tex]v_{x} = v_{o}\cdot \cos \theta[/tex]
[tex]v_{x} = 21.205\,\frac{m}{s}[/tex]
And the speed of the projectile is determined by Pythagorean Theorem:
[tex]v = \sqrt{v_{x}^{2}+v_{y}^{2}}[/tex]
[tex]v = \sqrt{\left(21.205\,\frac{m}{s} \right)^{2}+\left(-2.5\,\frac{m}{s} \right)^{2}}[/tex]
[tex]v \approx 21.352\,\frac{m}{s}[/tex]
The speed of the projectile after 4 seconds is approximately 21.352 meters per second.
c) By (1) we find the horizontal range of the projectile:
([tex]x_{o} = 0\,m[/tex], [tex]v_{o} \approx 42.410\,\frac{m}{s}[/tex], [tex]\theta = 60^{\circ}[/tex], [tex]g = -9.807\,\frac{m}{s^{2}}[/tex] and [tex]t = 8\,s[/tex])
[tex]x = 0\,m + \left(42.410\,\frac{m}{s} \right)\cdot (8\,s)\cdot \cos 60^{\circ}[/tex]
[tex]x = 169.64\,m[/tex]
The horizontal range of the projectile is 169.64 meters.
d) The projectile reaches its maximum height when velocity is zero. By (3) and knowing that [tex]v_{y} = 0\,\frac{m}{s}[/tex], [tex]v_{o} \approx 42.410\,\frac{m}{s}[/tex] and [tex]g = -9.807\,\frac{m}{s^{2}}[/tex], the time associated with maximum height is:
[tex]0\,\frac{m}{s} = \left(42.410\,\frac{m}{s}\right)\cdot \sin 60^{\circ}+\left(-9.807\,\frac{m}{s^{2}} \right) \cdot t[/tex]
[tex]t = 3.745\,s[/tex]
And by (2) and knowing that [tex]y_{o} = 20\,m[/tex], [tex]v_{o} \approx 42.410\,\frac{m}{s}[/tex], [tex]t = 3.745\,s[/tex], [tex]\theta = 60^{\circ}[/tex] and [tex]g = -9.807\,\frac{m}{s^{2}}[/tex], the maximum height reached by the projectile is:
[tex]y = 20\,m + \left(42.410\,\frac{m}{s} \right)\cdot (3.745\,s)\cdot \sin 60^{\circ}+\frac{1}{2}\cdot \left(-9.807\,\frac{m}{s^{2}} \right)\cdot (3.745\,s)^{2}[/tex]
[tex]y = 68.775\,m[/tex]
The maximum height of the projectile is 68.775 meters.
e) If we know that [tex]y_{o} = 20\,m[/tex], [tex]v_{o} \approx 42.410\,\frac{m}{s}[/tex], [tex]t = 8\,s[/tex], [tex]\theta = 60^{\circ}[/tex] and [tex]g = -9.807\,\frac{m}{s^{2}}[/tex], the components of the speed are, respectively:
[tex]v_{y} = \left(42.410\,\frac{m}{s}\right)\cdot \sin 60^{\circ} + \left(-9.807\,\frac{m}{s^{2}} \right)\cdot (8\,s)[/tex]
[tex]v_{y} = -41.728\,\frac{m}{s}[/tex]
[tex]v_{x} = v_{o}\cdot \cos \theta[/tex]
[tex]v_{x} = 21.205\,\frac{m}{s}[/tex]
And the speed of the projectile is determined by Pythagorean Theorem:
[tex]v = \sqrt{v_{x}^{2}+v_{y}^{2}}[/tex]
[tex]v = \sqrt{\left(21.205\,\frac{m}{s} \right)^{2}+\left(-41.728\,\frac{m}{s} \right)^{2}}[/tex]
[tex]v \approx 46.807\,\frac{m}{s}[/tex]
The speed of the projectile when it landed on the ground is approximately 46.807 meters per second.
Assume that Michael's teacher has a rule that if a student talks out-of-turn three times in one day, that student must stay in for recess for the
rest of the week. Which of the following methods is she using to control student behavior?
a. folkway
b. sociobiology
c. informal sanction
d. formal sanction
A basketball player jumps straight up with a speed of 14 m/s. How high did the player jump?
Answer:
The basketball player jumped 10 m high.
Explanation:
Vertical Launch Upwards
In a vertical launch upwards, an object is launched vertically up without taking into consideration any kind of friction with the air.
If vo is the initial speed and g is the acceleration of gravity, the maximum height reached by the object is given by:
[tex]\displaystyle h_m=\frac{v_o^2}{2g}[/tex]
The basketball player jumps up with a speed of vo=14 m/s. The maximum height is:
[tex]\displaystyle h_m=\frac{14^2}{2*9.8}[/tex]
[tex]\displaystyle h_m=\frac{196}{19.6}=10[/tex]
The basketball player jumped 10 m high.
The two types of biogenous sediments are calcareous ooze and _____ ooze.
Answer:
The two types of biogenous sediments are calcareous ooze and siliceous ooze
Explanation:
The table shows information about four objects resting at the top of a hill.
A 3-column table with 4 rows titled Four Objects at Rest on a Hill. The first column labeled Object has entries W, X, Y, Z. The second column labeled Mass (kilograms) has entries 50, 35, 62, 24. The third column labeled Potential Energy (Joules) has entries 980, 1029, 1519, 1176.
Which object is on the tallest hill?
W
X
Y
Z
It's Z your welcome :)
Answer:
It is Z i believe.
Explanation:
Potential Energy = mass x gravity x height
W: 980 = (50)(9.8)(h)
X: 1029 = (35)(9.8)(h)
Y: 1519 = (62)(9.8)(h)
Z: 1176 = (24)(9.8)(h)
simplify:
W: 980 = 490h
X: 1029 = 343h
Y: 1519 = 607.6h
Z: 1176 = 235.2h
Divide from both sides of each equation:
W: (980/490) = h
X: (1029/343) = h
Y: (1519/607.6) = h
Z: (1176/235.2) = h
Simplify the left side:
W: 2 = h
X: 3 = h
Y: 2.5 = h
Z: 5=h
A dragster finishes a race with a speed of 50 meters per second. The driver
deploys a drag chute which slows the car at a rate of -15 meters per second2.
Calculate the stopping distance of the dragster if only the drag chute is used
bring it to rest.
Answer:
83.3m
Explanation:
From the question we are given the following:
initial speed u = 50m/s
acceleration a = -15m/s²
final speed = 0m/s
Required
Stopping distance S
Using the equation of motion:
0² = 50²+2(-15)S
0² = 2500 - 30S
-2500 = -30S
S = 2500/30
S = 83.3m
Hence the stopping distance of the dragster if only the drag chute is used bring it to rest is 83.3m
Do you attract the earth or the earth attract you ?Which one is attracting with a large force ?You or the earth
———PLEASE HELP——— I NEED THE ANSWERS (ILL GIVE BRAINLIST)
Answer:
mountains, earthquakes, tsunamis
Explanation:
pain... physical, mental, emotional?
Define the term electrical resistance as applied to current electricity
Explanation:
Electrical resistance can be defined as the opposition to the flow of current in an electric circuit or wire. The resistance converts electrical energy into thermal energy, this serves as friction in mechanical systems. And this electrical energy converted to thermal is dissipated.
By ohm's law we have
Resistance R = Voltage V/ Current I
HELP PLEASE!!!
a crane lifts a 3,000 kg beam of concrete from the ground to a height of 50 m. what work is being done on the concrete?
Answer:
1,470,000Joules
Explanation:
Work done = Force * distance moves in the direction of the force
Given
mass = 3000kg
distance = 20m
Get the force
F = mg
F = 3000(9.8)
F = 29400N
Get the work done
Work done = 29400 * 50
Work done = 1,470,000Joules
Hence 1,470,000Joules work has been done on the concrete
what is electricity?
Explanation:
electricity is the flow of electrical power or charge
Explanation:
the flow of current is called electricity
give two differences between mass and weight
Answer: 1) Mass is a scalar quantity while weight is a vector quantity
2) Mass is measured in Gramma and kilogram while weight is measured in Newton.
Explanation:
Mass can be defined as the amount of matter that comprises an object. It is a scalar quantity, that is, it has magnitude. It is measured in kilogram with its unit in Kg. Mass is measured using an ordinary weighing scale.
Weight can be defined as the force acted upon an object due to gravity. Weight is a vector quantity, that is, it has both magnitude and direction towards the center of the earth. Weight can be measured with the use of a spring balance. Its unit is in Newton.
help me please ASAP
Answer:
F = 1200 [N]
Explanation:
Torque is defined as the product of force by Radius.
[tex]T=F*r[/tex]
where:
T = torque = 300 [N*m]
r = radius = 50/2 = 25 [cm] = 0.25 [m]
[tex]F=T/r\\F = 300/0.25\\F = 1200 [N][/tex]
The engine that moves the cables for the San Francisco cable cars delivers 390.3 kW of power for each line. How long does it take for 6.5 ×10^6 J of work (about the amount of work needed to raise a partially loaded cable car up Nob Hill) to be done by this engine?
Answer:
It would take 16.7 s for the work to be done by the engine.
Explanation:
From the question, given: Power = 390.3 kW
Work to be done = 6.5 x [tex]10^{6}[/tex] J
But, power and work done with respect to time, has a relationship of:
Power = [tex]\frac{work done}{time}[/tex]
So that,
time = [tex]\frac{work done}{Power}[/tex]
Thus,
time = [tex]\frac{6.5*10^{6} }{390.3*10^{3} }[/tex]
= 16.6539
time = 16.7 s
Time required is 16.7 seconds.
Thus, it would take 16.7 s for the work to be done by the engine.
A cart is moving at 55 m/s at an angle of 25° to the ground. Determine the horizontal component.
Answer:
The horizontal component of the velocity is 49.85 m/s.
Explanation:
Rectangular Components of a Vector
A 2D vector can be expressed in several forms. The rectangular form gives its two components, one for each axis (x,y). The polar form gives the components as the pair (r,θ) being r the magnitude and θ the angle.
When the magnitude and angle of the vector are given, the rectangular components are calculated as follows:
[tex]v_x=v\cos\theta[/tex]
[tex]v_y=v\sin\theta[/tex]
Where v is the magnitude of the vector and θ is the angle with respect to the x positive direction.
The cart is moving at v=55 m/s at θ=25°, thus:
[tex]v_x=55\cos 25^\circ[/tex]
[tex]v_x=49.85\ m/s[/tex]
The horizontal component of the velocity is 49.85 m/s.
Select the correct rocks.
Identify the igneous rocks.
Answer:
Red Volcano Rock and the Lava Rock Covered in Sulphur
Explanation:
Igneous Rocks are formed by volcanoes, lava, and magna. Sandstone is sedimentary and Slate is metamorphic. The other two are literally formed by volcanoes.
Answer:
Red Volcano Rock and the Lava Rock Covered in Sulphur
Explanation:
List the three main things necessary to build an electromagnet.
Answer:
Electromagnets are special types of magnets that are made by passing current through coils of wire. To make an electromagnet, the minimum requirements are:
1. A nail (usually made of iron, steel or zinc)
2. Dry cell batteries
3. Wire (Usually copper wire)
Other things could be:
1. Electric tape to hold both ends of the wire properly at the battery terminals.
2. Scissors to cut the wire into desired length.
3. Iron fillings for testing purposes.
Which element would Element X most likely be grouped with on the periodic table?
Answer:
group 0
Explanation:
it might be xenon (Xe)
According to the electronic configuration, and assuming the element to be halogen it is most likely to be grouped with potassium as halogens are in need of one electron which is easily made available by potassium.
What is electronic configuration ?Electronic configuration is defined as the distribution of electrons which are present in an atom or molecule in atomic or molecular orbitals.It describes how each electron moves independently in an orbital.
Knowledge of electronic configuration is necessary for understanding the structure of periodic table.It helps in understanding the chemical properties of elements.
Elements undergo chemical reactions in order to achieve stability. Main group elements obey the octet rule in their electronic configuration while the transition elements follow the 18 electron rule. Noble elements have valence shell complete in ground state and hence are said to be stable.
Learn more about electronic configuration,here:
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A square tile having 50cm side is made to withstand a pressure of 200N/m^2 find out if a force of 45N can be applied on the tile
Explanation:
Given that,
Side of a square tile, a = 50 cm = 0.5 m
Pressure withstand by it, P = 200 Pa
We know that,
Pressure = force/area
[tex]F=P\times A\\\\=200\times (0.5)^2\\\\=50\ N[/tex]
It is the force that tile withstand is 50 N. The force applied upon the time is 45 N. As 45 N can be applied on the tile because 45 N < 50 N.
Seafloor spreading is a process that occurs along ___________1____________. At ___________2____________ boundary, two plates move away from each other resulting to spreading of seafloor, thereby creating new ___________3____________ crust. Near the mid-oceanic ridge _________4__________ rocks are found and far from it are older.
Answer:
where is the answer choices
Explanation:
how can a simple machine lift a heavy load with smaller effort
Answer:
The axle is fixed to a frame or a block. The pulley is normally fixed to a support above the load. The load is tied to one end of the rope and the effort is applied at the other end. Such a pulley makes our work easier by simply changing the direction of the force, i.e. a load is lifted up using a downward effort.
May be this will help U
Answer:
The axle is fixed to a frame or a block. The pulley is normally fixed to a support above the load. The load is tied to one end of the rope and the effort is applied at the other end. Such a pulley makes our work easier by simply changing the direction of the force, i.e. a load is lifted up using a downward effort
Explanation:
what is the displacement of a cyclist who travels 1 mile north 1 mile east then finally 1 mile south
The displacement of a cyclist who travels 1 mile north 1 mile east then finally 1 mile south will be 1 mile in the east direction.
What is the displacement?A displacement is a vector in engineering and mechanics that has a length equal to the shortest route between a point P's initial and final positions.
The displacement is the vector quantity that depends on the magnitude as well as direction. And follows the law of vector addition.
The cyclist who travels 1 mile north 1 mile east then finally 1 mile south. Then the diagram is drawn below.
From the graph, the displacement is given as,
Displacement = 1 - 0
Displacement = 1 mile
The displacement of a cyclist who travels 1 mile north 1 mile east then finally 1 mile south will be 1 mile in the east direction.
Learn more about displacement:
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The diagram is a real world example of the first and second laws of thermodynamics. It shows how thermal energy is used to generate electricity. Which best describes how the diagram illustrates both laws of thermodynamics?
Answer:
First law: kinetic energy is used to turn an electric generator
Second law: some thermal energy is lost to the environment as it travels through the system
Explanation:
The first law of thermodynamics is known as the law of conservation of energy. It states that energy can neither be created nor destroyed but can only be transferred or changed from one form to another. When thermal energy is used to generate electricity, the kinetic energy of the steam is used to turn the electric generator (thereby producing electrical energy).
The second law of thermodynamics states that energy transfer or transformation leads to an increase in entropy resulting in the loss of energy. This law also states that as energy is transferred or transformed, some is lost in a form that is unusable. When thermal energy is used to generate electricity, some of the thermal energy is lost to the environment as it travels through the system.
Answer:
NOT A
Explanation:
Sorry I couldn't guess it right. Source EDGEN
PLEASE HELP!!
What does the electromagnet in an electric motor do?
A. It transforms mechanical energy into electrical energy.
B. It transforms magnetic force into electrical energy.
C. It transforms electrical energy into mechanical energy.
D. It transforms electrical energy into magnetic force.
Answer:
C. It transforms electrical energy into mechanical energy
Answer: C
Explanation:
What’s the substance that is formed as the result of a chemical reaction?
A. Chemical reaction
B. Catalyst
C. Activation energy
D. Collision theory
E. Products
F. Reactants
G. Reaction rate
Answer:
d
Explanation:
Yoga not only builds flexibility, but strength and balance.
True or False
Answer:
True
Explanation:
I just know.
One scientist is using an electromagnetic wave to map the dust between stars. The electromagnetic wave has shorter wavelength than radio waves but longer wavelength than visible light. What electromagnetic wave is the scientist using? X-ray Infrared light Gamma ray Ultraviolet radiation
Choose ALL that apply
Voltage
a)pushes free protons around a circuit
b)is measured in volts
c)causes current
d)pushes free electrons around a circuit
PLEASE ANSWER ASAP! It would be EXTREMELY appreciated if you could answer both. These are free responses, so try to make your answer somewhat original. Thanks in advance! And I will mark brainliest!
i need help finding the calculation for the bed forces if diagrams.