Question

Problem 31

Answer 1

Given information

Given a rescue plane wants to drop supplies to isolated mountain climbers on a rocky ridge  below. If the plane is travelling horizontally with a speed of . (Fig. 3-38)

To find: how far in advance of the recipients (horizontal distance) must the goods be dropped?

Step-by-step explanation

Step 1.

When the supplies are dropped, they follow a parabolic path and undergo projectile motion. Assuming that the air resistance is negligible, kinematic equations for two-dimensional motion can be used to get the horizontal distance before the area where the package should be dropped.

First, list all the given values. Since the object moves in a two-dimensional path, separate the quantities for the horizontal and vertical motion.

Even though the package is dropped relative to the person in the plane, it is initially moving with the plane. Therefore, when the package falls down, it is moving horizontally at a speed that is the same as that of the plane. Furthermore, this horizontal speed has a constant value since the horizontal acceleration is zero. Let the initial horizontal position of the point where the package was dropped be  .