A projectile is shot vertically into the air with an initial velocity of Assuming that...

A projectile is shot vertically into the air with an initial velocity of Assuming that air resistance is proportional to the square of the instantaneous velocity, the motion is described by this pair of differential equations:

Positive y – axis up, origin at ground level and

Positive y-axis down, origin at the maximum height so that at y = h. The first and second equations describe the motion of the projectile when rising and falling, respectively.

(a) Determine the limiting, or terminal, velocity of the falling projectile. Compare this terminal velocity with that obtained in Problem 27 in Exercises 3.2.

(b) Prove that the impact velocity of the projectile is less than the initial velocity . It can also be shown that the time needed to attain its maximum height h is less than the time that it takes to fall from this height. See Figure 3.25.