a ping pall ball is dropped from 20m on a horizontal roof of a house and always reduce to 1/8of previous fall in each bounce .what height does it fall in 7th time
Well, well, well, it seems our ping pall ball is quite the bouncy little fella! Let's calculate how high it falls on its seventh bounce.
So, starting from a height of 20m, we can see that the ball reduces to 1/8 of its previous fall with each bounce. That's quite the diminishing effect!
Let's crunch the numbers:
Bounce 1:
Height = 20m * (1/8) = 2.5m
Bounce 2:
Height = 2.5m * (1/8) = 0.31m
Bounce 3:
Height = 0.31m * (1/8) = 0.039m
Bounce 4:
Height = 0.039m * (1/8) = 0.0049m
Bounce 5:
Height = 0.0049m * (1/8) = 0.00061m
Bounce 6:
Height = 0.00061m * (1/8) = 0.000076m
Bounce 7:
Height = 0.000076m * (1/8) = 0.0000095m
Ta-da! After bouncing a total of seven times, our ping pall ball plummets down to a height of approximately 0.0000095 meters. That's so tiny, it practically disappears! Better keep an eye out for it, or you might just step on it without even realizing.
To find the height at which the ping pong ball falls in the 7th bounce, we can use the following formula:
height of nth bounce = initial height × (reduction factor)^(n-1)
Given that the initial height is 20m and the reduction factor is 1/8, we can substitute these values into the formula:
height of 7th bounce = 20m × (1/8)^(7-1)
Simplifying this equation, we have:
height of 7th bounce = 20m × (1/8)^6
Now, let's calculate the height of the 7th bounce:
height of 7th bounce = 20m × (1/8)^6
= 20m × (1/64)
= 0.3125m
Therefore, the height at which the ping pong ball falls in the 7th bounce is approximately 0.3125 meters.
To determine the height the ping pong ball falls in the 7th bounce, we can use the concept of geometric progression.
First, let's find the initial height of the ball after the first bounce:
Starting from a height of 20m, the ball falls and then bounces back to 1/8th of its previous height.
Height after the first bounce: 20m * (1/8) = 2.5m
Now, let's find the height of the ball after the second bounce:
The ball is dropped from a height of 2.5m and then bounces back to 1/8th of its previous height.
Height after the second bounce: 2.5m * (1/8) = 0.3125m
We can observe a pattern in the heights after each bounce:
1st bounce: 2.5m
2nd bounce: 0.3125m
3rd bounce: 0.0391m
4th bounce: 0.0049m
5th bounce: 0.0006m
6th bounce: 0.0001m
Now, to find the height after the 7th bounce, we continue the pattern:
7th bounce: 0.0001m * 1/8 = 0.0000125m
Therefore, the ball falls to a height of 0.0000125m (or 1.25 cm) in the 7th bounce.
If you mean that its bounce is 1/8 less each time, then 20 * (7/8)^7
If you mean that each bounce is 1/8 as high as the previous bounce, then 20 * (1/8)^7