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.
I used the same method as Charlie did, once I realized that the key (for me) is taking the frame reference as the car window, not the disc. A person sitting inside the car would see the disc coming at an angle.
After doing the trig solution (see Charlie's), I tried another way:
After drawing a diagram and right triangle, one sees that the apparent velocity of the disc as viewed by the person in the car is the vector sum of the velocities of the car and the disc. Since the window is 3 times the width of the disc, this "apparent velocity" must be three times the disc velocity. So, if the velocities of the Disc and Car are D and C, and the Apparent velocity is A, we have:
A^2 = C^2 + D^2 and also
A = 3D, so
9 D^2 = C^2 + D^2
8 D^2 = C^2
D = (C/4) * sqrt(2)
and again as in Charlie's solution,
Disc speed = 250 * sqrt(2) ~= 353.55 cm/sec
Posted by Larry
on 2014-10-02 12:08:33