Question

A ball of mass 0.4 Kg is kicked straight up with (initial) speed 20m/sec. Find the highest point on the ball trajectory and the time needed
for the ball to reach it. The air resistance force is proportional to the velocity
and is equal to
gamma= 0.48 at the speed 1 m/sec. For simplicity, assume that the acceleration due to gravity is equal to
g= 10m/sec^2

Answer 1

F=ma = m(dV/dt)=- mg-\[\gamma\] *v so make it a first order linear differential equation : dv/dt +[\gamma\]v/m=g ???

Answer 2

Looks good. \[F = ma\]\[m {dv \over dt} = - mg - \gamma v \rightarrow dv = \left [-g - {\gamma v \over m} \right ] dt\]\[\int\limits_{v_0}^{v_f} dv = \int\limits_{t_0}^{t_f} \left [ -g - {\gamma v \over m} \right] dt\]\[(v_f - v_0) = -g t_f - {\gamma v \over m} t_f\]Note that \(v_f = 0\).