Find velocity given mass

Question

You throw a 0.8 kg dodgeball at the head of a 30 kg 5th grader at rest. The ball is traveling at 9 m/s before it hits the student and has slowed to 2 m/s as it bounces off of them. With what velocity will the child’s head whip back?

Answer 1

Given:

M_B = 0.8 kg

M_H = 30 kg

V_B = 9 m/s

V_H = 0 m/s

V_B' = -2 m/s

Find

V_H' =?

Solution

Apply conservation of momentum

M_BV_B+M_HV_H = M_BV_B'+M_HV_H'

M_BV_B = M_BV_B'+M_HV_H'

M_BV_B - M_BV_B' = M_HV_H'

M_B (V_B - V_B') = M_HV_H'

(M_B (V_B - V_B'))/M_H' = V_H'

V_H' = 0.8 * (9 - (-2))/30 = 0.293 m/s (to the right)

***Please note the bounce back velocity of the ball is negative because it bounces to the left, changes direction after impact***

Answer 2

You throw a 0.8 kg dodgeball at the head of a 30 kg 5th grader at rest. The ball is traveling at 9 m/s before it hits the student and has slowed to 2 m/s as it bounces off of them. With what velocity will the child’s head whip back?

Since the mass of the head is not stated, the speed of the head may be difficult to determine. Lets solve as if the entire 5th grader will be set in motion by the ball.

Total momentum of the system before collision = total momentum of the system after collision

The system consists of the ball and the 5th grader.

so [0.8kg x 9m/s] + [30kg x 0m/s] = [0.8kg x (-2m/s)] + [30kg x Vm/s]

7,2kgm/s - (-1.6kgm/s) = 30V kgm/s

8.8kgm/s/30kg = 0.3m/s in the direction the ball was initially thrown

Mr. A