Suppose that a falling hailstone with density δ = 1 starts from rest with negligible radiu...

Suppose that a falling hailstone with density δ = 1 starts from rest with negligible radius r = 0. Thereafter its radius is r = let (k is a constant) as it grows by accretion during its fall. Use Newton’s second law-according to which the net force F acting on a possibly variable mass m equals the time rate of change dp/dt of its momentum p = mv − to set up and solve the initial value problem

where m is the variable mass of the hailstone, v = dy/dt is its velocity, and the positive y-axis points downward. Then show that dv/dt = g/4. Thus the hailstone falls as though it were under one-fourth Lhe influence of gravity.