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1. Use the net force equation and the fact that F = ma to write a differential equation for the ball’s velocity.

2. Assume m = .5kg and p = .1. Make a direction field for the differential equation and sketch a solution of the initial value problem v(0) = 50 m/s.

3. Solve the initial value problem algebraically. Hint: be sure to take the constant of integration into account.

4. Find an equation of the height of the ball at time t.

5. When does the ball reach the apex of its trajectory? When does the ball land?

6. Does it take the ball longer to come up or come down?

This is what I've done so far.

m(dv/dt) - pv - mg = 0 for the upward motion

and

m(dv/dt) + pv - mg = 0 for the downward motion

taking upward to be positive (and both p, g < 0).