# Finding speed of stone when it hits the ground.

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1. Oct 2, 2015

### justinm326

1. The problem statement, all variables and given/known data
A small rock is thrown upward with a speed of 30ft/s from the edge of a building 200ft above the ground. What is the speed of the rock when it hits the ground? Use acceleration due to gravity as –32ft/s squared.

2. Relevant equations
integral of acceleration= v(t)
integral of v(t)= position

3. The attempt at a solution
I know that v(t)=30, the initial position is 200 and acceleration=-32 and I know the problem is asking for the velocity of the rock, I visualize this problem under the interval [a,b] so it's asking for the velocity at b when the rock hits the ground. I just have no idea how all of the information fits together to set up an integral equation. Any help with this initial set up would be great

2. Oct 2, 2015

### andrewkirk

Problems like this are easier to solve using energy conservation. You just equate the final kinetic energy (KE) to the initial KE plus initial potential energy (PE). You use PE = mgh where h is height and m is mass, and KE $\frac{1}{2}mv^2$.

Are you allowed to use energy?

3. Oct 2, 2015

### HallsofIvy

You are told that the acceleration is a constant -32 ft/sec^2 so dv/dt= -32 or dv= -32dt. That should be a very easy integration. Further dx/dt= v (where x is height above the ground). Once you know v(t), that will be an easy integration.

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