What is the velocity and angle of impact when throwing a rock off a cliff?

  • Thread starter kingofretards
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So the initial angle is 90 degrees. We can then use trigonometry to find the angle of impact, which will be equal to the angle between the horizontal and vertical components of the velocity.
  • #1
kingofretards
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Homework Statement


A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 23.0 m/s. The cliff is h = 22.0 m above a flat horizontal beach.

1. How long after being released does the stone strike the beach below the cliff?

2. With what speed and angle of impact does the stone land?


Homework Equations


So far, I've only used this equations:
y-y0=v0y*t-.5*g*t^2

I couldn't find any other equations.

The Attempt at a Solution


I've solved the first part already, the time the stone strikes the beach is 2.1 seconds.
But I'm still stuck on the second part, as I'm confused about which equations to use.
 
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  • #2
Try calculating the vertical speed of the rock after a time of 2.1 seconds.
Combine this vertical component of the velocity with the horizontal component given in the question. You may want to draw a quick right-angled triangle with one side equal to the horizontal component and another equal to the vertical component. The hypotenuse of this triangle will give you the speed. The angle of impact is simply the angle between the horizontal component and the vertical component.
 
  • #3
You have to be sure that you separate your x and y components. If the rock is being thrown horizontally, v0x = 23.0 m/s and v0y = 0 m/s. See what I mean? You will have to use trig to find the final velocity (usually the inverse tangent of vy and vx).

Some other useful functions (I've written them in the x direction here, but they hold for the y direction as well):
vx = v0x + axt
vx2 = v0x2 + 2ax(x - x0)
 
  • #4
If so, what is the angle? I couldn't find any angles at all. It says the speed and angle at impact (when it hits the ground), not at start. So how can I find them?

I still don't understand it.
 
  • #5
The angle at which the stone was thrown was given in your initial question.
 
  • #6
If you are throwing something horizontally, the throw is at a right angle to the ground.
 

1. How does the height of the cliff affect the distance the rock travels?

The height of the cliff does not have a direct impact on the distance the rock travels, but it does affect the time it takes for the rock to reach the ground. The higher the cliff, the longer the rock will be in the air and the farther it will travel horizontally before hitting the ground. This is due to the force of gravity pulling the rock down at a constant rate.

2. What factors influence the distance the rock travels?

The distance the rock travels is primarily influenced by the initial velocity or speed at which the rock is thrown off the cliff. Other factors that may affect the distance include air resistance, the shape and weight of the rock, and wind speed and direction.

3. Does the angle at which the rock is thrown affect its distance?

Yes, the angle at which the rock is thrown off the cliff can have a significant impact on its distance. The optimal angle for maximum distance is 45 degrees, as this allows for a balance between the vertical and horizontal components of the rock's motion, resulting in the longest distance travelled.

4. Can a rock thrown off a cliff ever come back to the same spot?

In theory, yes, a rock thrown off a cliff can come back to the same spot if it is thrown at a specific angle and with enough initial velocity. This is known as a projectile's maximum range and is calculated using the projectile motion equations. However, in practical situations, it is highly unlikely for a rock to land in the exact same spot due to external factors such as wind and air resistance.

5. How does the mass of the rock affect its distance?

The mass of the rock does not have a significant impact on its distance. According to the law of inertia, the mass of an object does not affect its motion unless an external force is applied. Therefore, assuming the rock is thrown with the same initial velocity, a heavier rock will travel the same distance as a lighter rock.

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