IBM Ponder This #035 · March 2001

Suggested by Mike Cargiulo

We're playing golf in the Tyrolean Alps.
The air is so thin up here that air resistance is negligible.
And the course is laid out a bit strangely...

The first hole is 150 yards, due horizontal.
(The cup is on the same vertical level as the tee.)
We hit the ball at top speed, at the correct angle to maximize distance, and find that it precisely reaches the cup. Hole in one.

The second hole is also 150 yards, but due vertical: the cup is directly below the tee.
This time we require no force at all: we can merely drop the ball into the cup.

The third hole is a bit tricker: 150 yards, at a 45 degree angle below the horizon. At what angle should we hit the ball, and at what speed (as a percentage of the speed required on the first hole), if we wish to minimize the speed required?

David Buller (age 11) has a clever solution to the problem as stated:

	Simply give the ball a very slight nudge (so the speed is essentially zero).  Gravity will take the ball rolling down the hill for a hole-in-one.  So the answer is speed=0 and angle=-45 degrees.

The rest of you, let's restrict ourselves to a ball exactly hitting the cup at the end of its parabolic arc, without rolling. Thanks, David.

Solution

Best opened after a real attempt

To be added.