Help me on this physics problem?

Question

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 to the ground is 1.4 s. Find the time it takes for the ball to fall from rest all the way to the ground.

not jsut answers

and explanation

i'm trying to learn and do HW

Answer 1

I'll call the original height of the wrecking ball H and the time it takes to fall all the way to the ground T.

The expression for the height of the ball at any time t is given by

y = H - 1/2 g t^2

so I can write two specific versions of this for times 1.4s and T:

At 1.4s y has to be half of H --

H/2 = H -1/2 g (1.4s)^2

At t =T y must be zero (it's on the ground) --

0 = H - 1/2 g T^2

Now I can plug in g = 9.8 m/s^2 and I have two equations in the two unknowns H and T.  They can be solved simultaneously.  I use QuickMath to save work.  It gives

H=19.208 m

T = 1.9799 s

Answer 2

1/2*s=1/2*g*t^2

s=g*t^2

=9.8 * (1.4^2) = 19.208 "total distance of fall"

from s=1/2*g*t^2

solve for t:

t=sqr(2*s/9.8) "total time of fall"

total fall time time=sqr((19.5 * 2) / 9.8) = 1.99489 s

=

time it takes for the ball to fall from rest all the way to the ground.: