A helicopter traveling upward at 120 m/s drops a package from a height of 500 meters. To the nearest second how long does it take to hit the ground?

Answer 1

I believe that there is mistake in your given data: the velocity has to be 12 m/s

There are two motions of the package:
1. upward motion with the initial velocity of 12 m/s
h=vₒ²/2g =144 /2•9.8 =7.34 m
H=500+7.34 =507.34 m
2. Dowmward motion (free fall)
t=sqrt(2H/g)=sqrt(2•507.34/9.8) =10.18 s.
If the speed is 120 m/s, calculate using your numbers.