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## Homework Statement

A beach ball is thrown upwards with initial speed v0. The drag force is given by Fd = −mαv for a drag coefficient α and speed v.

(a) the height h reached

(b) Show that the height may be expressed in terms of the final speed when the ball strikes the ground vf

(c)Finally show that the total time taken for the ball to travel up and back down is given by T = (v0 + vf )/g.

## Homework Equations

## The Attempt at a Solution

I solved DE for V

$$\dot{V} = \alpha V}+{g}$$

get $$t=\frac{1}{\alpha}ln(\frac{\alpha V_0 +g}{g})$$

and DE for h $$\ddot h -\alpha \dot h = g$$

get $$h = \frac{gln(\frac{\alpha V_0 +g}{g})}{\alpha ^2}+C_1\frac{g}{\alpha V_0 +g}+C_2$$

There is the problem, I can only find initiail value of ##t=0##, which does not solve the 2 constants. Is there another point of time I should use? Or there is something I did wrong?

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