In order to determine the time taken, we will use the following formula:
s = ut + 0.5at²
Where s is the distance traveled, u is the initial velocity, a is the acceleration and t is the time. Now, because the ball is dropped, the initial velocity is 0. Moreover, the distance the ball must travel is 100 feet. And the acceleration due to gravity is 32.17 ft/s². Plugging these values in:
100 = 0*t + 0.5 * 32.17 * t²
t = √(200/32.17)
t = 2.49 seconds
The basketball will take 2.49 seconds to hit the ground.
