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