A golf ball cannon is made that shoots the ball at a 45 degree angle to the horizontal, and consistently achieves 300 yards.

That cannon is transported to a spherical asteroid which has the same density as the Earth. A golf ball is fired in a horizontal direction and just reaches the velocity for a stable circular orbit.

What is the radius of the asteroid?
What is the time of one orbit?

Assume the radius of the Earth is 4000 miles.
(Inspired by The Longest Drive)

(In reply to re: solution question by Mindrod)

The asteroid probably has a slight rotation, not enough to affect the calculation significantly, but enough so that the cannon is no longer there when the ball comes around next.

At a 26 mile radius, the asteroid has considerably more mass than the golf ball, so I'd agree the asteroid's reaction would be negligible.

The major fiction in the solution is the assumption that the 300 yard range on earth is not the result of a considerable reduction due to air resistance.  The muzzle velocity is really probably significantly higher than was calculated, in order to compensate for this air resistance.

Posted by Charlie on 2006-02-19 10:10:48