To solve this problem, we can use the kinematic equation for vertical motion:
h = ut + (1/2)gt^2
where: h = height (distance) fallen u = initial velocity g = acceleration due to gravity (approximately -32 feet per second squared) t = time
In this case, the height fallen is 96 feet, the initial velocity is 16 feet per second, and the acceleration due to gravity is -32 feet per second squared. We need to find the time it takes until the diver enters the water, so we can set h = 0 and solve for t.
0 = ut + (1/2)gt^2
0 = 16t + (1/2)(-32)t^2
0 = 16t - 16t^2
Rearranging the equation:
16t^2 - 16t = 0
Factor out 16t:
16t(t - 1) = 0
This equation has two solutions: t = 0 and t = 1. However, t = 0 represents the initial time when the diver is still on the ledge, so we can ignore that solution.
Therefore, the diver will enter the water after 1 second.