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Classical Mechanics

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Moderate

Spring-Launched Ball

CLMECH-O5HDJY

A ball of mass $m$ is launched vertically into the air by a spring with constant $k$. If the spring was compressed $x$ meters prior to launching the ball and air resistance with an average force $F$ acts on the ball, what is the equation for the maximum height, $h$ of the ball? Assume the compression of the spring is much smaller than the maximum height of the ball.

A

$h = \cfrac{kx^2}{2(mg + F)}$

B

$h = \cfrac{kx^2}{2mg}$

C

$h = \cfrac{\frac{1}{2}kx^2 - F}{mg}$

D

$h = \cfrac{\frac{1}{2}kx^2 - mg}{F}$