Question

When a ball is dropped it bounces and then rises. The ball rises to 90% of the height from which it is dropped. The ball is dropped from a height of 4m. A) calculate the height of the rises after the first bounce. B) calculate the height of the rise after the second bounce. The ball carries on bouncing each time rising to 90%of the last rise C) for how many bounces does it rise to height greater than 1m

Answer 1

A) 3.6 meters

B) 3.24 meters

C) 13 Times

Step-by-step explanation:

:)

Answer 2

The height of the first bounce is 3.6m. The height of the second bounce is 3.24m. The ball rises to a height greater than 1m after 7 bounces.

Step-by-step explanation:

(a) To calculate the height of the first rise, we can multiply the initial height by 90% (0.9) since the ball rises to 90% of the height from which it is dropped. So, the height of the first bounce is 4m × 0.9 = 3.6m.

(b) Similarly, for the second bounce, we multiply the height of the first bounce (3.6m) by 90% (0.9) to get the height of the second bounce: 3.6m × 0.9 = 3.24m.

(c) To determine how many bounces result in a height greater than 1m, we can set up an inequality. Each bounce is 90% of the previous bounce, so we can represent the height after n bounces as 4m × (0.9)ⁿ. We want this height to be greater than 1m, so we set up the inequality: 4m × (0.9)ⁿ > 1m. Solving for n, we find that n > 7.

Therefore, the ball rises to a height greater than 1m after 7 bounces.