height h on nth bounce is
64/2^n
when n=8, h=1/4
please help me
64/2^n
when n=8, h=1/4
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.
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.