This is a perfect application for the general formula for the height of an object in gravity at any time:
Height = (original height)
+ (original velocity x time)
- (1/2 x gravity x time²)
H = H₀ + v₀T - 1/2 G T²
In this helicopter problem:
H₀ = 125 m
v₀ = 5.52 m/s
G = 9.8 m/s²
and we want to find 'T' when the package hits the ground.
That's the time when H=0 .
H₀ + v₀T - 1/2 G T² = 0
125 + 5.52T - 4.9T² = 0
Using the quadratic formula:
T = -5.52 ± √[5.52² + (4 x 4.9 x 125) ] all over (-9.8)
= -5.52 ± √2480.47 all over (-9.8)
= 0.563 ± 5.082
T = -4.52
T = 5.65
In a real-world situation, we ignore the negative solution.
The package hits the ground 5.65 seconds after being released.
I hope there was nothing fragile inside.
