HMMT 2004 K5
- Calculus
- Answer
A mouse is sitting in a toy car on a negligibly small turntable. The car cannot turn on its own, but the mouse can control when the car is launched and when the car stops (the car has brakes). When the mouse chooses to launch, the car will immediately leave the turntable on a straight trajectory at 1 meter per second.
Suddenly someone turns on the turntable; it spins at 30 rpm . Consider the set of points the mouse can reach in his car within 1 second after the turntable is set in motion. (For example, the arrows in the figure below represent two possible paths the mouse can take.) What is the area of , in square meters?
Dataset text NuminaMath olympiads. Quoted with source.
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\pi / 6
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