Paper 4, Section I, A

Galileo releases a cannonball of mass $m$ from the top of the leaning tower of Pisa, a vertical height $h$ above the ground. Ignoring the rotation of the Earth but assuming that the cannonball experiences a quadratic drag force whose magnitude is $\gamma v^{2}$ (where $v$ is the speed of the cannonball), find the time for it to hit the ground in terms of $h, m, \gamma$ and $g$, the acceleration due to gravity. [You may assume that $g$ is constant.]

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