A ball is thrown vertically into the air with unknown velocity v0 at time t = 0. Assume th...

A ball is thrown vertically into the air with unknown velocity v0 at time t = 0. Assume that the ball is thrown from about shoulder height, say y0 = 1.5 m. If you ignore air resistance, then it is easy to show that dv/dt = –g, where g = 9.8m/s2 is the acceleration due to gravity. Follow the lead of exercise to show that vdv = –gdy. Further, because the velocity of the ball is zero when it reaches its maximum height,

Find the initial velocity of the ball if the ball reaches a maximum height of 15 m.

Next, let’s include air resistance. Suppose that R(v) = –rv and show that the equation of motion becomes

If the mass of the ball is 0.1 kg and r = 0.02 N/(m/s), find the initial velocity if the ball is again released from shoulder height (y0 = 1.5m) and reaches a maximum height of15 m.