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## Homework Statement

A ball is thrown vertically upwards at speed v

_{0}. Assume drag force is proportional to v

^{2}.

a) Show that, while moving upwards, Newton's Second Law gives a = -g(1+v

^{2}/v

_{t}

^{2}) where v

_{t}is the terminal speed.

b) Take v

_{0}= 3v

_{t}and solve for v(t),

**the time t**and

_{max}at which it reaches max height**the maximum height it reaches**. Express your results in terms of g and v

_{t}

## Homework Equations

a = -g(1+v

^{2}/v

_{t}

^{2})

v = -v

_{t}tanh (t/T), where T = v

_{t}/g

y = -v

_{t}

^{2}/g * ln [cosh (gt/v

_{t})]

## The Attempt at a Solution

I got part A of the question simple enough, I'm having trouble with part B. I got the expression for v(t) which was the integral of the first equation. I'm having trouble looking for t

_{max}and the max height. It sounds simple enough but I can't grasp around the idea on how to do it.