A player attempts to throw a 30 cm diameter flying disc at the open window of a moving car. The car is traveling at a velocity of 1000cm/sec and the disc will travel perpendicular to the car and to the direction of motion of the car. If the window is a rectangle 90 cm wide and the disc is parallel to the ground, how fast will the disc have to travel to make in cleanly through the window?
Feel free to make any necessary assumptions.
Relative to the car window as a frame of reference, the open window can be represented in cross-section as a line segment which forms the hypotenuse of a right triangle, one of whose legs is the diameter of the disk. The other leg and its continuation and a line parallel to it form the trajectories of the outer rim of the disk. The larger this angle makes with the car-window line, the faster the disk needs to be going. At 45° it must be going at the same speed as the car; at 90° it would be going infinitely fast. Clearly the speed of the disk is 1000 times the tangent of this angle. And the angle in the given case is arcsin(30/90).
1000 * tan(arcsin(1/3)) ~= 353.553390593274 cm/sec.
Posted by Charlie
on 2014-09-25 19:13:59