How far out should the supplies be dropped?

Question

An airplane needs to drop a package of supplies in a remote location (landing is not possible). The plane is flying 86.9m above the ground at a speed of 158.8 m/s. We know that the plane should NOT drop the package when it is passing directly over the location. Instead, the plane needs to drop the supplies before it reaches the location. How far out (IN METERS) should the supplies be dropped ? ( in other words, how far horizontally will the package go as it falls?) ignore air resistance

Answer 1

Thinking ONLY about what happens in the vertical direction, There is no initial vertical velocity (the plane is only moving in the horizontal direction. Therefore, from a vertical perspective this is just like free fall and y = 1/2gt² or t = √(2y/g) = √(2•86.9/9.81) = 4.209 seconds (assuming g = 9.81 m/s²)

Now, thinking ONLY in the horizontal direction, the plane will travel at 158.8 m/s for 4.209 seconds so to find the distance, we multiply velocity and time to get 668.41 m. If we assume 3 significant figures, that rounds to 668 m.

Answer 2

Hello Kayla!

The reasoning of this problem is that the time to reach the ground must be the same time the package reaches the destination.

The time to reach the ground is given by the equation:

S = S₀ + v₀*t + at²/2

86.9 = 0 + 0 + 10t²/2 (here I considered a = 10 m/s² and the initial horizontal speed as 0)

t = 4.17 s

Now let's look at the horizontal speed. The speed of the package is the same of the airplane, 158m/s.

So the distance must be:

d = t*v = 4.17*158 = 658.7 m

Feel free to ask anything. Best wishes!