A tennis ball is dropped from a height of 32 feet, rebounding to 1/2 its former height with each bounce. How far will the ball have traveled VERTICALLY when it comes to a rest?
infinite geometric series
a1 = 32
r = .5
sum = a1 (1 - r^n) / (1-r)
= 32 (1 - .5^oo) /(1 - .5)
=32 /.5 = 64
wait a minute that ignored the up parts
32 + 16 + 16 + 8 + 8 + 4 + 4 .....
32 + 2 ( 16)/.5
= 32 + 64 = 96
atmospheric pressure decreases as you go higher and,it decreases 20% as for every 1000m.
given that the pressure at sea level is about 1013hpa.
what would the pressure be at 8,848m high?
To find the total vertical distance traveled by the tennis ball when it comes to a rest, we need to sum up the distances traveled during each bounce.
Let's break down the problem step by step:
1. The ball is dropped from a height of 32 feet, so the first bounce starts at this height.
2. During the first bounce, the ball rebounds to 1/2 its former height, which is 32 * (1/2) = 16 feet.
3. The next bounce starts at a height of 16 feet.
4. During the second bounce, the ball rebounds to 1/2 its former height, which is 16 * (1/2) = 8 feet.
5. The next bounce starts at a height of 8 feet.
6. We continue this process until the ball comes to a rest, which occurs when the height reaches zero.
Now, let's sum up the distances traveled during each bounce:
First bounce: 32 feet
Second bounce: 16 feet
Third bounce: 8 feet
Fourth bounce: 4 feet
Fifth bounce: 2 feet
Sixth bounce: 1 foot
To find the total distance, we add up these distances:
32 + 16 + 8 + 4 + 2 + 1 = 63 feet
Therefore, the tennis ball will have traveled 63 feet vertically when it comes to a rest.