Putnam 1939 A6

Take either (i) or (ii). (i) A circle of radius $a$ rolls on the inner side of the circumference of a circle of radius $3 a$ . Find the area contained within the closed curve generated by a point on the circumference of the rolling circle. (page 105) (ii) A shell strikes an airplane flying at a height $h$ above the ground. It is known that the shell was fired from a gun on the ground with a muzzle velocity of magnitude $V$ , but the position of the gun and its angle of elevation are both unknown. Deduce that the gun is situated within a circle whose center lies directly below the airplane and whose radius is $\frac{V}{g} \sqrt{V^{2}-2 g h}$ (Neglect the resistance of the atmosphere.)

Dataset text PutnamGAP. Quoted with source.

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