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 8 kg is given an upward initial velocity of 20 m/sec and then allowed to fall under the influence of gravity. Assume that the force in newtons due to air resistance is -16y, where y is the velocity of the object in m/sec. Determine the equation of motion of the object. If the object is initially 100 m above the ground, determine when the object will strike the ground.

Solution:Step 1:The objective of this question first we have to determine the equation of motion of the object. If the object is initially 100 m above the ground, determine when the object will strike the ground.Step 2:Given that:Mass = m = 8 kg.Initial velocity = v0 =20 m/sec.Step 3:Expect that the force in newtons because of air resistance is - 16y, where y is the speed of the protest in m/sec. That is F1 = -16y.The force because of the gravity is F2 = -mg, here g is the gravitational drive because of the earth space. Along these lines, the net force following up on the question is:F= F1+ F2..Step 4:According to the Newton’s second law, that we havePut the value of m and g, we get= -8(9.8) -16y Divide the equation by 8= -9.8 - 2y