Question

A tennis ball is released from a height of 2.0 m above the floor, and then bounces three times. With each bounce, dissipative forces cause it to lose 16.0% of its mechanical energy. How high does it reach after the third bounce?

12 cm

120 cm

140 cm

120 mm

Answer 1

The height reached by the tennis ball after the third bounce, considering a 16% energy loss with each bounce from an initial height of 2.0 meters, is approximately 120 cm.

Step-by-step explanation:

The question deals with the mechanics of a bouncing ball and the conservation of energy, specifically the loss of mechanical energy due to dissipative forces. When a tennis ball is released from a height of 2.0 meters, and it loses 16% of its mechanical energy on each bounce, the height it reaches after the third bounce can be calculated by successively reducing the height by 16%. After the first bounce, the ball reaches 84% of its original height (2.0 m), so:

• Height after 1st bounce: 2.0 m × 0.84 = 1.68 m
• Height after 2nd bounce: 1.68 m × 0.84 = 1.4112 m
• Height after 3rd bounce: 1.4112 m × 0.84 = 1.185408 m

Since the options are not precise to the calculated value, we must round the answer to 120 cm (1.2 meters), since it is the closest option to the calculated height after the third bounce.