Question

A relief plane is flying over a desert island to drop supplies to the research crew stationed there. The plane is flying 1150 m above the sea level and releases the relief package 2750 m away from the island. The package has a parachute on it, which slows the downward acceleration down to 5.0 m/s^2. How fast does the plane have to be moving in order to ensure the package lands where it needs to? R​

Answer 1

128 m/s

Step-by-step explanation:

Take down to be positive.

Given:

Δx = 2750 m

aₓ = 0 m/s²

Δy = 1150 m

v₀ᵧ = 0 m/s

aᵧ = 5.0 m/s²

Find: v₀ₓ

First, find the time it takes for the package to fall:

Δy = v₀ᵧ t + ½ aᵧ t²

1150 = (0) t + ½ (5) t²

1150 = 2.5t²

t = 21.4 s

Now find the initial horizontal velocity of the package:

Δx = v₀ₓ t + ½ aₓ t²

2750 = v₀ₓ (21.4) + ½ (0) (21.4)²

v₀ₓ = 128 m/s