Question

A helicopter is ascending vertically with a speed of 5.52 m/s . At a height of 125 m above the Earth, a package is dropped from the helicopter. How much time does it take for the package to reach the ground?

Answer 1

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.