After each bounce, a ball reaches 1/2 the height of the previous bounce. First to second bounce = 1 second. How long between the second and the third bounce?
Thanks
h = (1/2) g t^2
h/2 = (1/2) g T^2
so
2 T^2= t^2
T^2 = t^2/2
T = t/sqrt 2 = .707 sec
Well, if the first height is "H," the second height would be 1/2 H. Then, the third height would be 1/2 of 1/2 H, or 1/4 H. Since the time between the first and second bounce is 1 second, it seems like the ball is in quite a hurry to get back up in the air. So, if we assume the same amount of time passes between each bounce, I would estimate that it takes about 1/2 second between the second and third bounce. That's one speedy ball!
To find out how long it takes between the second and third bounce, we need to understand the pattern of the time intervals between the bounces.
Based on the information provided, after each bounce, the ball reaches half the height of the previous bounce. Since the time between the first and the second bounce is 1 second, we can deduce that the ball takes the same amount of time to go up as it takes to come back down (assuming no air resistance).
Therefore, the total time for the first bounce is 1 second, with half the time spent going up and the other half coming back down. This means the time it takes for the ball to go up is 0.5 seconds.
Now, for the second bounce, the ball first needs to go up half the height of the previous bounce, which takes 0.5 seconds. Then, it needs to come back down, which also takes 0.5 seconds. So the total time for the second bounce is 1 second.
Following the same logic, the time it takes for the ball to go up for the third bounce is 0.5 seconds, and the time it takes for the ball to come back down is 0.5 seconds.
Therefore, the total time between the second and third bounce is the same as the time it takes for one full bounce, which is 1 second.
So, the answer to your question is that it takes 1 second between the second and third bounce.
.50seconds
no my bad
its 30 seconds.