A 0.060 kg ball hits the ground with a speed of –32 m/s. The ball is in contact with the ground for 45 milliseconds and the ground exerts a +55 N force on the ball.

Use the impulse–momentum relationship: the change in velocity is force times contact time divided by mass. The ground’s impulse is (55 N)(0.045 s) = 2.475 kg·m/s, so the velocity changes by 2.475 ÷ 0.060 = 41.25 m/s. Starting at −32 m/s, the final velocity is −32 + 41.25 = 9.25 m/s, which rounds to 9.3 m/s.

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