A bat moving at 90 km/h strikes an oncoming ball moving at 110 km/h. If the batter follows through so that the speed of the bat doesn't change during the hit and the coefficient of restitution of the ball is 0.6, what speed does the batted ball have after it has been struck?
A) 66 km/h
B) 200 km/h
C) 20 km/h
D) 210 km/h

Question

Quizplus · Accepted Answer

The speed of the batted ball can be calculated using the coefficient of restitution formula: $e = \frac{v_2 - v_1}{u_1 - u_2}$, where $e$ is the coefficient of restitution (0.6), $v_2$ is the final velocity of the ball, $v_1$ is the final velocity of the bat (90 km/h, since it doesn't change), $u_1$ is the initial velocity of the bat (90 km/h), and $u_2$ is the initial velocity of the ball (-110 km/h, since it's moving towards the bat). Rearranging the formula to solve for $v_2$, we get $v_2 = e(u_1 - u_2) + v_1$. Substituting the given values, $v_2 = 0.6(90 - (-110)) + 90 = 0.6(200) + 90 = 120 + 90 = 210$ km/h.

A Bat Moving at 90 Km/h Strikes an Oncoming Ball