A boy plays with a ball and he drops it from a height of 1.5 m. Every time the ball hits the ground, it bounce

Question

A boy plays with a ball and he drops it from a height of 1.5 m. Every time the ball hits the ground, it bounces back to attain a height 4 / 5th of the previous height. The ball does not bounce further if the previous height is less than 50 cm. What is the number of times the ball hits the ground before the ball stops bouncing?

Accepted Answer

The problem asks us to calculate the number of times a ball hits the ground before its bounce height falls below 50 cm.

1.  Convert all units to centimeters for consistency:
    Initial height = 1.5 m = 150 cm.
    Stopping threshold = 50 cm.

2.  Calculate the height after each bounce:
    *   Initial drop height = 150 cm.
    *   After 1st hit: Bounces to 150 cm * (4/5) = 120 cm. (Since 120 cm > 50 cm, it will bounce again).
    *   After 2nd hit: Bounces to 120 cm * (4/5) = 96 cm. (Since 96 cm > 50 cm, it will bounce again).
    *   After 3rd hit: Bounces to 96 cm * (4/5) = 76.8 cm. (Since 76.8 cm > 50 cm, it will bounce again).
    *   After 4th hit: Bounces to 76.8 cm * (4/5) = 61.44 cm. (Since 61.44 cm > 50 cm, it will bounce again).
    *   After 5th hit: Bounces to 61.44 cm * (4/5) = 49.152 cm. (Since 49.152 cm is less than 50 cm, the ball will not bounce further after this hit).

3.  The ball stops bouncing after the 5th hit because the height it attains (49.152 cm) is less than the 50 cm threshold.

Therefore, the ball hits the ground 5 times before it stops bouncing.

The final answer is B

Answer

4

Answer

5

Answer

6

Answer

7

Explanation

Related questions