# Falling Object Rebound

Can someone please explain to me how to calculate the rebound velocity, rebound acceleration, and rebound height of an object of mass=m dropped from height=h? Thank you.

• Do you know the coefficient of restitution of the ground and ball ? – Tausif Hossain Jun 13 '17 at 6:11
• Can you please add more details and what you've tried? – QuirkyTurtle98 Jun 13 '17 at 6:18
• @quirkyturtle98 - I've tried ALOT of googling but most information is related to before impact or at impact and not much is out there about the post impact dynamics – PhysicsMakesTheWorldGoRound Jun 13 '17 at 6:35
• @ Tausif Hossain - Thanks for your help. Unfortunately, I dont know the coefficient of restitution. Any good sources that you can recommend or ways to determine it empirically? – PhysicsMakesTheWorldGoRound Jun 13 '17 at 6:38

The coefficient of restitution,$e$ is: $$e=\frac{v_(rebound)}{v_(impact)}$$ Thus if you know $e$ then you can find rebound velocity.( Notice if collision is perfectly elastic then e=1 and rebound velocity = impact velocity and rebound height= original height)
For rebound height just use $v^2=u^2+2gh$ to find $h_(after-rebound)$ setting $v=0$ and $u=v_(rebound)$. Now to find the acceleration you need to know the collision time between object and ground. Then acceleration,$a$ is simply given by : $$a=\frac{v_(impact)+v_(rebound)}{Collision Time}$$