Show that a ball dropped from a height h feet reaches the floor in 14h−−√ seconds. Then use this result to find the time, in seconds, the ball has been bouncing when it hits the floor for the first, second, third and fourth times:

Complete Question

"We might think that a ball that is dropped from a height of 15 feet and rebounds to a height 7/8 of its previous height at each bounce keeps bouncing forever since it takes infinitely many bounces. This is not true! We examine this idea in this problem.

Show that a ball dropped from a height h feet reaches the floor in 1/4√h seconds. Then use this result to find the time, in seconds, the ball has been bouncing when it hits the floor for the first, second, third and fourth times:

t = ¼√h seconds

Step-by-step explanation:

Given

Height = 15 feet

Show that a ball dropped from a height h feet reaches the floor in 14h−−√ seconds. Then use this result to find the time, in seconds, the ball has been bouncing when it hits the floor for the first, second, third and fourth times:

From this, we understand that

u = Initial Velocity = 0

a = g = acceleration due to gravity = 9.8m/s² = 32ft/s²

h = initial height = 15

Using Newton equation of motion

h = ut + ½at²

Substitute the values

15 = 0 * t + ½ * 32 t²

15 = 16t² make t² the subject of formula

t² = 15/16 square root both sides

t = √15/√16

t = ¼√15

But h = 15

So, t = ¼√h seconds

Or t = 0.25√h seconds

-- Proved

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