Question

1. A Red Cross airplane is going to throw supplies to a small island. As captain of the plane, you must throw the package with the supplies at the right moment so that it doesn’t fall on the ocean.

If the plane is traveling at 60 m/s at an altitude of 500 m, at what distance from the island should you drop the supplies. Ignore friction.

In answering this question, include the following:

- What is this kind of motion called?

- Sketch the trajectory of the package. Indicate coordinate axes and label the sketch with the given information.

- Calculate the answer (algebra first)

- Assess the answer.

Answer 1

This is a projectile motion.

The velocity of the package will be same as that of the plane at the time of separation

v_x = 60 m/s (purely horizontal)

The initial vertical component of the velocity, u_y = 0

Let the time taken by the package to reach the ground = t

For vertical motion

y = u_yt + 1/2gt²

500 = 0 + 0.5 x 10 x t²

t = 10 seconds

During this time the horizontal distance travelled by the package

R = v_x x t

R = 60 x 10

R = 600m

So package must be dropped 600m before the actual target.