A child drops a ball from a window.The ball strikes the ground in 3.0 seconds.What is the velocity of the ball the instant before it hits the ground?

hi, let me try to answer it for you.

there are 2 methods you can use to solve this problem. you can choose which one you preferred.
anyway, first we need to know the height.
to find it use the equation of:
[tex]h= v_{0}t+ \frac{1}{2}g t^{2} [/tex]
which v0 is the initial velocity (obviously zero as the child dropped it)
t is the time in second, g is the gravitational acceleration let say 10 m/s^2
hence the height will be:
[tex]h=0*3+ \frac{1}{2}*10* 2^{2} [/tex]
h=45 meters

now we can use the concept of mechanical energy:
[tex] \frac{1}{2}m v^{2}=mgh [/tex]
let us kill the m term, as both side have it, then:
[tex]v= \sqrt{2gh} [/tex]
such that v=30 m/s

another way, we can use this equation:
[tex] v_{t} ^{2} =v_{0} ^{2}+2gh [/tex]
with vt is the velocity at some point. v0 will be zero and hence:
[tex] v_{t}= \sqrt{2gh} [/tex]
which also give 30 meters.

hope it helps :D