how do i work out the following word problem. a particular ball retains half of its heght on each bounce when dropped from a height of 80 m. give the height of the ball on the fifth bounce after being dropped?(will the ball comes to rest?)
bounce - distance covered
1 ---- 80
2 --- 2(40) ....... twice, because it goes up and down
3 --- 2(20)
4 --- 2(10)
5 --- 2(5)
take it from there
To work out the height of the ball on the fifth bounce, we need to first understand the pattern of how the height changes with each bounce.
Given that the ball retains half of its height on each bounce, we can calculate the height after each bounce using the formula:
height_after_bounce = initial_height / 2^n
where n is the number of bounces.
In this case, the initial height is 80 m and we want to find the height after the fifth bounce. Let's calculate it step by step:
On the first bounce, the height is: 80 / 2^1 = 80 / 2 = 40 m
On the second bounce, the height is: 80 / 2^2 = 80 / 4 = 20 m
On the third bounce, the height is: 80 / 2^3 = 80 / 8 = 10 m
On the fourth bounce, the height is: 80 / 2^4 = 80 / 16 = 5 m
On the fifth bounce, the height is: 80 / 2^5 = 80 / 32 = 2.5 m
So, the height of the ball after the fifth bounce is 2.5 meters.
As for whether the ball comes to rest, the answer depends on the context and specific conditions. If we assume that the ball follows the given pattern indefinitely, the ball will approach zero height with each subsequent bounce but will never technically come to rest. In reality, other factors such as air resistance and energy loss would eventually cause the ball to come to a stop.