A ball is dropped from a height of 36 m. The ball bounces back 70 % of the distance it falls. To what height does the ball bounce after the 6th bounce? Round answers to one decimal place.
help!
bounce = 7/10 of previous Hight
by a/1-r
36/1-7/10
36*10/3
120 m
To find the height to which the ball bounces after the 6th bounce, we can use the following steps:
1. Calculate the initial height of the ball after the 1st bounce.
- The ball falls from a height of 36 m, so after the 1st bounce, it reaches a height of 36 * 0.7 = 25.2 m (since it bounces back 70% of the distance it falls).
2. Calculate the subsequent heights after each bounce.
- After each bounce, the ball reaches a height that is 70% of the previous height. So, after the 2nd bounce, the height would be 25.2 * 0.7 = 17.64 m. After the 3rd bounce, the height would be 17.64 * 0.7 = 12.348 m, and so on.
3. Repeat the calculation for each bounce until the 6th bounce.
- Continuing the pattern, after the 4th bounce, the height would be 12.348 * 0.7 = 8.6436 m. After the 5th bounce, it would be 8.6436 * 0.7 = 6.05052 m.
Therefore, after the 6th bounce, the ball would reach a height of approximately 6.1 meters (rounded to one decimal place).
after 1st bounce, height = 36(.7) = 36(.7)^1
after 2 bounces, height = [36(.7)](.7) = 36(.7)^2
..
after 6 bounces, height = ...... = ......
You do it, I will not give you the answer.