Question

Problem 32

Answer 1

Given information

Given the horizontal distance of  in advance of the mountain climbers, (Fig. 3-39).

To find: What vertical velocity (up or down) should the supplies be given so that they arrive precisely at the climbers' position? With what speed do the supplies land?

Step-by-step explanation

Step 1.

When the supplies are released, 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 initial vertical velocity and the final speed.

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

The package 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  .

Meanwhile, the pull of gravity causes it to accelerate down with a magnitude of  . Let all values of height be measured from the ground where  .