physics
posted by nj .
A wrecking ball is hanging at rest from a crane when suddenly the cable breaks. The time it takes for the ball to fall halfway is 1.6 seconds. Find the time it takes for the ball to fall from rest all the way to the ground.

For constant acceleration with 0 initial velocity, the distance is:
distance = (1/2) (acceleration)(time^2)
If D= the total distance to the ground:
D = (1/2)g(TotalTime^2)
(1/2)D=(1/2)g(MidpointTime^2)
or
(1/2)g(TotalTime^2)= 2[(1/2)g(MidpointTime^2)]
(TotalTime^2) = 2(MidpointTime^2)
the problem states MidpointTime=1.6s
Substitute and solve for the total time
d=1/2at^2
a is the acceleration of gravity, t is given as 1.6s. Plug those in and solve for d. The problem states that is halfway.