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 βππ.
28. How high will the ball bounce on the 4th bounce
A. 8β
27
B. 27β
8
C. 2β
3
D. 3β
2
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. 27β/8.
To determine how high the ball will bounce on the 4th bounce, we need to calculate the height after each bounce using the given information that the ball bounces by 2/3 of its initial bounce.
Let's start by calculating the initial bounce height:
Initial bounce height = βππ
Now, to calculate the height after the 1st bounce:
Height after 1st bounce = (2/3) * Initial bounce height
To calculate the height after the 2nd bounce:
Height after 2nd bounce = (2/3) * Height after 1st bounce
To calculate the height after the 3rd bounce:
Height after 3rd bounce = (2/3) * Height after 2nd bounce
Finally, to calculate the height after the 4th bounce:
Height after 4th bounce = (2/3) * Height after 3rd bounce
So, the option that represents the height after the 4th bounce is:
C. 2β/3
Therefore, the correct answer is C. 2β/3.