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Putnam 1958 B6

Session B

A projectile moves in a resisting medium. The resisting force is a function of the velocity and is directed along the velocity vector. The equation $x$ $=f(t)$ gives the horizontal distance in terms of the time $t$ . Show that the vertical distance $y$ is given by $y=-g f(t) \int \frac{d t}{f^{\prime}(t)}+g \int \frac{f(t)}{f^{\prime}(t)} d t+A f(t)+B$ where $A$ and $B$ are constants and $g$ is the acceleration due to gravity.

Dataset text PutnamGAP. Quoted with source.

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