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

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Homework Help Overview

The problem involves a student throwing a stone horizontally from a cliff, with the goal of determining the time until impact, as well as the speed and angle of impact upon hitting the ground. The subject area includes kinematics and projectile motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss calculating the vertical speed after a specific time and combining it with the horizontal speed to find the resultant velocity. There are suggestions to visualize the components using a right-angled triangle. Some participants emphasize the importance of separating the x and y components of motion and using trigonometric functions to find the angle of impact.

Discussion Status

The discussion is ongoing, with participants providing guidance on how to approach the calculation of the vertical speed and resultant angle. There are questions regarding the interpretation of the angle of impact, indicating some confusion about the problem's requirements.

Contextual Notes

Participants note the initial conditions of the problem, including the horizontal throw and the lack of vertical initial velocity. There is also mention of the need to clarify the angle of impact as distinct from the angle of the throw.

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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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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.
 
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)
 
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.
 
The angle at which the stone was thrown was given in your initial question.
 
If you are throwing something horizontally, the throw is at a right angle to the ground.
 

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