Answer to Question #196163 in Mechanics | Relativity for Donna

Question

Prove collision (of tennis ball) was elastic with a Velocity - time graph (Tip: calculate the distance)

Answer 1

Kinematic equations for objects in free-fall:

$v=v_0-gt$

$y=y_0+v_0t-gt^2/2$

Let $v_0=0,y_0=10$

Then:

$v=-9.8t$

$y=10-4.9t^2$

$t=\sqrt{10/4.9}=1.43\ s$ -the ball falls on the ground

After collision equations become:

$v=9.8(t-1.43)$

$y=4.9(t-1.43)^2$

From graphs we can see that the ball falls on the ground after $1.43\ s$ , and after the same time it rises to the height of $10\ m$. So, the collision is elastic.