Physics- falling objects, parabola shape

[havechanged]

Hey! I know that the horizonal and horizontal motion are unrelated, and the velocity remains the same (if there is no air resistance, friction etc)- this correlates with the whole 'shooting a gun and dropping a bullet at the same time, which one will hit the ground first? They will fall at the same time.' However, I don't know how to find the different parts of a problem.

For example:

A stone is thrown horizontally at a speed of 10 m/s from the top of the cliff 78.4 cm high. How long does it take the stone to reach the bottom of the cliff? How far from the base of the cliff does the stone strike the ground?

How also, if needed, would I find how fast a ball is going if it ended up going X far off a cliff X high? Or, how would I find how high the cliff is if I have the other two pieces of data?

Thanks!

 

[Chi Meson]

Originally posted by havechanged


A stone is thrown horizontally at a speed of 10 m/s from the top of the cliff 78.4 cm high. How long does it take the stone to reach the bottom of the cliff? How far from the base of the cliff does the stone strike the ground

I assume you meant to say that you know that "vertical" and horizontal motion are independent.

The amount of time the stone remains in the air depends entirely on the vertical motion. It would take the same amount of time to hit the ground as if it were dropped. SO, can you calculate how long it would take a stone to drop straight down? THis the amount of time your stone is in the air, and so it is also the amount of time it is moving at 10 m/s in the horizontal direction. Now you have v and t. FInd d.

 

[M98Ranger]

It's great that you have a basic understanding of the relationship between horizontal and vertical motion. To solve problems like the one you mentioned, we can use the equations of motion which relate the distance, time, and acceleration of an object. In this case, since the stone is experiencing constant acceleration due to gravity, we can use the equation d = v0t + 1/2at^2, where d is the distance traveled, v0 is the initial velocity (in this case, the horizontal velocity of 10 m/s), a is the acceleration due to gravity (9.8 m/s^2), and t is the time.

To find the time it takes for the stone to reach the bottom of the cliff, we can set d = 78.4 cm (0.784 m) and solve for t. This will give us the time it takes for the stone to fall vertically. To find the distance from the base of the cliff where the stone strikes the ground, we can use the same equation, but this time set d = 78.4 cm + the distance from the base of the cliff. This will give us the total distance traveled by the stone, and we can solve for the distance from the base of the cliff.

To find the initial velocity of the ball if it traveled a certain distance off a cliff, we can use the same equation, but this time set d = the distance traveled and solve for v0. And to find the height of the cliff if we have the other two pieces of data, we can use the same equation, but this time set d = the total distance traveled and solve for the height.

I hope this helps! It's important to remember to always use the correct units in these equations and to pay attention to the direction of motion. Good luck!