Problem 1E

Problem

Unless otherwise stated, in the following problems we assume that the gravitational force is constant with g = 9.81 m/sec2 in the MKS system and g = 32 ft/sec2 in the U.S. Customary System.

An object of mass 5 kg is released from rest 1000 m above the ground and allowed to fall under the influence of gravity. Assuming the force due to air resistance is proportional to the velocity of the object with proportionality constant b = 50 N-sec/m, determine the equation of motion of the object. When will the object strike the ground?

Step 1 </p>

In this problem, we are asked to find the equation of motion and the time taken by the object to strike the ground.

Step 2</p>

The given values are

It is given that the force due to air resistance (drag force) is proportional to the velocity of the object with proportionality constant.

Therefore .

Step 3</p>

The buoyancy force (while falling downwards) acts downwards whereas the drag force acts upwards.Therefore the total force will be .

Therefore