(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A stone with weight w is thrown vertically upward into the air from ground level with initial speed v_{0}. If a constant force f due to air drag acts on the stone throughout its flight, (a) show that the maximum height reached by the stone is

[tex] h = \frac{v_0^2}{2g(1+f/w)} [/tex]

(b) Show that the stone's speed is

[tex] v = v_0 \left( \frac{w-f}{w+f} \right) ^ {1/2} [/tex]

just before impact with the ground.

2. Relevant equations

work done by an external force = change in energy

3. The attempt at a solution

I have no trouble with part (a). I need help with (b)

[tex]\begin{align*}

W_{air} &= (-f) * (2h) \\

&= -2fh \\

&= -2f\frac{v_0^2}{2g(1+f/w)} \\

& = -2f\frac{v_0^2 w}{2g(w+f)}

\end{align*}[/tex]

[tex]W_{air} = \Delta E = \Delta K = \frac{1}{2}m(v^2 - v_0^2) = \frac{w}{2g}(v^2 - v_0^2)[/tex]

We can set the two expressions equal

[tex]\begin{align*}

-2f\frac{v_0^2 w}{2g(w+f)} &= \frac{w}{2g}(v^2 - v_0^2) \\

-2f\frac{v_0^2 }{(w+f)} &= v^2 - v_0^2 \\

v^2 &= v_0^2 + -2f\frac{v_0^2 }{w+f} \\

&= v_0^2 \left( \frac{1-2f}{w+f} \right)

\end{align*}[/tex]

But this is wrong. Can anyone tell me where I messed up?

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# Homework Help: Conservation of energy problem (projectile with air drag)

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