A ball is dropped from a height of 16 feet and always rebounds 0.25 of the distance fallen.How high did it rebound the 5th time?
Well, if the ball rebounds 0.25 of the distance fallen each time, that means on the first bounce it rebounded 16 feet * 0.25 = 4 feet.
On the second bounce, it rebounded 4 feet * 0.25 = 1 foot.
On the third bounce, it rebounded 1 foot * 0.25 = 0.25 feet.
On the fourth bounce, it rebounded 0.25 feet * 0.25 = 0.0625 feet.
So, by the time we reach the fifth bounce, the ball rebounded a height of... drumroll, please... 0.0625 feet.
Guess the ball isn't exactly setting any high-jump records! *badum-tss*
To find out how high the ball rebounded on the 5th time, we can use the given information that the ball rebounds 0.25 of the distance fallen.
Let's calculate the distance fallen on the 5th bounce:
1st bounce: Distance fallen = 16 feet (initial drop from a height of 16 feet)
2nd bounce: Distance fallen = 16 * 0.25 = 4 feet (rebound from the 1st bounce)
3rd bounce: Distance fallen = 4 * 0.25 = 1 foot (rebound from the 2nd bounce)
4th bounce: Distance fallen = 1 * 0.25 = 0.25 feet (rebound from the 3rd bounce)
5th bounce: Distance fallen = 0.25 * 0.25 = 0.0625 feet (rebound from the 4th bounce)
Therefore, the ball rebounded a height of 0.0625 feet on the 5th bounce.
To find out how high the ball rebounded on the 5th time, let's first calculate the distance it rebounded each time.
Given that the ball rebounds 0.25 of the distance fallen, the distance it rebounds will be decreasing progressively with each rebound.
On the first rebound, it rebounds 0.25 times the distance fallen, which is 0.25 * 16 = 4 feet.
On the second rebound, it falls from a height of 16 feet minus the 4 feet rebounded, which is 16 - 4 = 12 feet. It then rebounds 0.25 times this distance, which is 0.25 * 12 = 3 feet.
On the third rebound, it falls from a height of 12 feet minus the 3 feet rebounded, which is 12 - 3 = 9 feet. It then rebounds 0.25 times this distance, which is 0.25 * 9 = 2.25 feet.
On the fourth rebound, it falls from a height of 9 feet minus the 2.25 feet rebounded, which is 9 - 2.25 = 6.75 feet. It then rebounds 0.25 times this distance, which is 0.25 * 6.75 = 1.6875 feet.
Finally, on the fifth rebound, it falls from a height of 6.75 feet minus the 1.6875 feet rebounded, which is 6.75 - 1.6875 = 5.0625 feet.
Therefore, the ball rebounded approximately 5.0625 feet on the fifth rebound.
The rebound height is a geometric sequence, i.e.
H(n)=H0*r^n
where n=number of bounces.
For H0=16', r=0.25
H(1)=16*(0.25)^1=4'
H(2)=16*(0.25)²=1'
...