This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

1941 Putnam, B5
Tags: velocity
A car is being driven so that its wheels, all of radius $a$ feet, have an angular velocity of $\omega$ radians per second. A particle is thrown off from the tire of one of these wheels, where it is supposed that $a \omega^{2} >g$. Neglecting the resistance of the air, show that the maximum height above the roadway which the particle can reach is $$\frac{(a \omega+g \omega^{-1})^{2}}{2g}.$$

1956 Putnam, A3
Tags: physics , velocity
A particle falls in a vertical plane from rest under the influence of gravity and a force perpendicular to and proportional to its velocity. Obtain the equations of the trajectory and identify the curve.