I launch a ball vertically precisely 8' in the air. Then I launch a ball vertically 10' in the air. How much longer will it take the ball to travel 10' versus 8'? Put differently, how much more time does it take the ball to go the 2' further (travelling up and returning down)?
To determine the time it takes for the ball to travel a certain height, we can use basic physics equations. The time it takes for an object to reach its peak height and return to the ground is directly related to the vertical distance traveled.
The time it takes for an object to reach its peak height (in this case, 8') and return to the ground can be calculated using the equation:
t = √(2d/g)
Where,
t is the time taken,
d is the vertical distance traveled (8' or 10'), and
g is the acceleration due to gravity (approximately 32.2 ft/s²).
Let's calculate the time for the first scenario where the ball is launched to a height of 8':
t1 = √(2*8/32.2) ≈ 0.892 seconds
Now, let's calculate the time for the second scenario where the ball is launched to a height of 10':
t2 = √(2*10/32.2) ≈ 1.040 seconds
To find out the difference in time, we subtract t1 from t2:
Δt = t2 - t1 = 1.040 - 0.892 ≈ 0.148 seconds
Therefore, the ball takes approximately 0.148 seconds longer to travel an additional 2 feet (10' vs. 8').