Fay's rubber ball bounces exactly half the height from which it is dropped. she drops the ball from the top of a building that is 64 meters tall. how high will the ball bounce on its eight bounces?
please help me
height h on nth bounce is
64/2^n
when n=8, h=1/4
64×(2^n)=h
To find the height the ball will bounce on its eight bounces, we need to determine how the height changes after each bounce.
Given that the ball bounces exactly half the height from which it is dropped, we can set up the following sequence:
1st bounce: 64 meters * 0.5 = 32 meters
2nd bounce: 32 meters * 0.5 = 16 meters
3rd bounce: 16 meters * 0.5 = 8 meters
4th bounce: 8 meters * 0.5 = 4 meters
5th bounce: 4 meters * 0.5 = 2 meters
6th bounce: 2 meters * 0.5 = 1 meter
7th bounce: 1 meter * 0.5 = 0.5 meters
8th bounce: 0.5 meters * 0.5 = 0.25 meters
Therefore, the ball will bounce to a height of 0.25 meters on its eighth bounce.
To find out how high the ball will bounce on its eighth bounce, we need to understand the pattern of its bounces.
Since the ball bounces exactly half the height from which it is dropped, we can use the following equation to determine the height of each bounce:
Height of bounce = (1/2) * Height of previous bounce
Given that the ball is dropped from a building that is 64 meters tall, the height of the first bounce would be:
Height of first bounce = (1/2) * 64 = 32 meters
To find the height of the second bounce, we use the same equation:
Height of second bounce = (1/2) * Height of previous bounce
Height of second bounce = (1/2) * 32 = 16 meters
We can continue this pattern to find the height of subsequent bounces:
Height of third bounce = (1/2) * Height of previous bounce
Height of third bounce = (1/2) * 16 = 8 meters
Height of fourth bounce = (1/2) * Height of previous bounce
Height of fourth bounce = (1/2) * 8 = 4 meters
Height of fifth bounce = (1/2) * Height of previous bounce
Height of fifth bounce = (1/2) * 4 = 2 meters
Height of sixth bounce = (1/2) * Height of previous bounce
Height of sixth bounce = (1/2) * 2 = 1 meter
Height of seventh bounce = (1/2) * Height of previous bounce
Height of seventh bounce = (1/2) * 1 = 0.5 meters
Finally, for the eighth bounce:
Height of eighth bounce = (1/2) * Height of previous bounce
Height of eighth bounce = (1/2) * 0.5 = 0.25 meters
Therefore, the ball will bounce to a height of 0.25 meters on its eighth bounce.