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:
Answer:
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
