A ball is hit straight upward with a velocity of 2 m/s. The mass of the ball is 0.05 kg. The air resistance (that slows down the ball) is proportional to its velocity (v) at any given time and is mathematically expressed as 0.5v. a. Derive an ODE for the velocity of the ball as a function of time. b. How long does it take to reach it's maximum height? c. If the ball was hit from an initial height of 1 m, what is the max height it could reach?