A projectile of mass m = 0.11 kg shot vertically upward with initial velocity v(0) = 8 m/s is slowed due to the force of gravity, Fg = −mg, and due to air resistance, Fr = −kv|v|, where g = 9.8 m/s2 and k = 0.002 kg/m. The differential equation for the velocity v is given by
mv' = −mg − kv|v|.
a. Find the velocity after 0.1, 0.2. . . 1.0s.
b. To the nearest tenth of a second, determine when the projectile reaches its maximum height and begins falling.