Velocity of rubber ball when it strikes to the ground,
v0=√2gh0 Using the formula of coefficient of restitution,
e=| velocity after collision |
| velocity before collision |
⇒e=⇒e= ⇒v1=e√2gh0...(i)
As, initial height of the ball
=h0.
∴ The first height of the rebound,
h1= ⇒h1=e2h0 [Using Eq. (i)]
The nth height of the ball to the rebound,
hn=⇒hn=e2nh0 The velocity of the ball after
nth rebound,
vn=env0 Now, the total distance travelled by the ball after nth rebound is
H=h0+2h1+2h2+2h3... H=h0+2e2h0+2e4h0+2e6h0... H=h0[1+2e2(1+e2+e4+e6...)] Using the formula,
1+e2+e4+...= ⇒H=h0[1+2e2()] ⇒H=h0() ⇒H=5()(∵e2==) H=47.6m Now, the total time taken by the ball to come to rest
T=t0+2t1+2t2+... T=√+2√+2√+... T=√[1+2e+2e2+...] T=√[1+2e(1+e+e2+...)] T=19s The average velocity,
vavg == =2.5m∕s Hence, the average velocity is
2.5m/s.