Question

A super ball bounces by 2
3
of its initial bounce when
dropped on a hard surface. If it is dropped from a
height of ℎ𝑐𝑚.
28. How high will the ball bounce on the 4th bounce
A. 8ℎ
27
B. 27ℎ
8
C. 2ℎ
3
D. 3ℎ
2

Answer 1

The height of the ball after each bounce can be written as a geometric sequence with a common ratio of 2/3:

h, (2/3)h, (2/3)^2h, (2/3)^3h, ...

So the height of the ball after the 4th bounce is:

(2/3)^3h = 8h/27

Therefore, the answer is B. 27ℎ/8.