1. A ball with mass m is thrown at speed v from zero height on level ground.

(a) At what angle should it be thrown so that the area under the trajectory is maximum?

(b) At what angle should it be thrown so that the trajectory length is maximum?

(c) Re-derive (a) and (b) considering now a drag force acting on the ball, namely F = mv.

2. A body of mass m falls from rest in an uniform gravitational field through the atmosphere, which exerts on the body a drag force given by F = mv², where v is the vertical velocity, and > 0 is the drag constant. Find the variation of the body's velocity and position with time.