IBM Research | Ponder This | March 2001 challenges

Ponder This

March 2001

<<February March April>>

Ponder This Challenge:

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.

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Challenge: 03/01/01 @ 9:00 AM EST
Solution: 03/30/01 @ 9:30 PM EST
List Updated: 03/30/01 @ 9:30 AM EST

Henry Bottomley (03.01.2001 @ 10:57 AM EDT)

Aron Fay (03.01.2001 @ 11:18 AM EDT)
Derek Kisman (03.01.2001 @ 1:45 PM EDT)
Marian Olteanu (03.01.2001 @ 2:04 PM EDT)
John Hamilton (03.01.2001 @ 2:18 PM EDT)
Colin Bown (03.01.2001 @ 2:24 PM EDT)
Sorin Ostafiev (03.01.2001 @ 8:10 PM EDT)
Dharmashankar Subramanian (03.01.2001 @ 10:39 PM EDT)
Ionel Santa (03.02.2001 @ 5:58 AM EDT)
Francis Golding (03.02.2001 @ 6:25 AM EDT)
Ionut Breaz (03.02.2001 @ 8:06 AM EDT)
Michael Malak (03.02.2001 @ 10:14 AM EDT)
Daniel Bitin (03.02.2001 @ 12:28 PM EDT)
Andrew Froggatt (03.03.2001 @ 12:11 PM EDT)
Ming Song (03.03.2001 @ 3:03 PM EDT)
Dave Biggar (03.04.2001 @ 8:22 AM EDT)
Prithu (03.04.2001 @ 12:10 AM EDT)
Ariel Landau (03.04.2001 @ 8:30 AM EDT)
Dieter Verhofstadt (03.05.2001 @ 5:12 AM EDT)
Vince Lynch (03.05.2001 @ 3:51 PM EDT)
Xuan Baldauf (03.05.2001 @ 9:08 PM EDT)
Stephane Higueret (03.06.2001 @ 3:49 AM EDT)
Christie Bolton (03.06.2001 @ 3:50 PM EDT)
Krishna Kumar (03.07.2001 @ 10:56 AM EDT)
Karthikeyan Bhasyam (03.07.2001 @ 12:23 PM EDT)
Prabhat Agarwal (03.07.2001 @ 1:28 PM EDT)
Darryl Buller (03.07.2001 @ 4:29 PM EDT)
Jonathan Wildstrom (03.07.2001 @ 6:55 PM EDT)
C A Subramanian (03.07.2001 @ 10:36 PM EDT)
Douglas Schrag (03.08.2001 @ 10:20 AM EDT)
Shmuel Spiegel (03.08.2001 @ 12:08 PM EDT)
Vic Monell (03.08.2001 @ 3:50 PM EDT)
Alexey Vorobyov (03.09.2001 @ 3:54 AM EDT)
Nicusor Timneanu (03.09.2001 @ 9:57 AM EDT)
Joshua Zirbel (03.09.2001 @ 3:59 PM EDT)
Mihai Cioc (03.11.2001 @ 2:10 PM EDT)
Paul Thomas (03.11.2001 @ 9:27 PM EDT)
Ralf Seliger (03.14.2001 @ 1:34 PM EDT)
Scott Ruland (03.19.2001 @ 9:43 AM EDT)
Marco Aiello (03.21.2001 @ 7:22 PM EDT)
Ross Millikan (03.22.2001 @ 5:16 PM EDT)
Jesus Sanz (03.23.2001 @ 9:18 AM EDT)
Paul Vandenkeybus (03.24.2001 @ 8:41 AM EDT)
Brian Bitto (03.27.2001 @ 3:48 AM EDT)
Steve Walter (03.27.2001 @ 10:49 AM EDT)

Attention: If your name is posted here and you wish it removed please send email to the ponder@il.ibm.com.