## ________________

A little physics never hurts, and team member Jamal brings in two puzzles for the team to ponder.

## ________________

### Mining Mishap

A miner was partway up a 10-foot ladder in an even taller vertical shaft when he saw a rock far above him beginning to fall from a stationary position, to the side of the ladder. He instantly began climbing up at his top speed of 4 feet per second, reaching the top of the ladder just as the rock arrived there. He later determined that if he had climbed down from his original spot at 4 feet per second, he would have reached the bottom of the ladder just as the rock arrived there. Use the acceleration of gravity as g = 32 feet per second squared.

How far up the ladder was he when the rock started to fall?

### Pulley Puzzle

The ideal pulley system shown at left has weightless and frictionless elements except for the weights shown. Initially all 3 weights are held in place. Then they are all released simultaneously.

In the first moments after the release of all three weights from rest, will the 99-weight start to go up, go down, or stay at rest?

## Solutions to week 122

In Minimum Racket Wear, one hit will do. For Rolling Circles, the smaller disk must execute 13 full rotations.

Minimum Racket Wear answer explained:
Each time Rafa serves, he swings and misses twice to lose the point; each time his opponent serves, he misses, giving Rafa the point without any hit from Rafa. They carry on this way until Rafa serves at 6-5 or 7-6 in the tiebreak game. Then he serves an ace to win the set. One hit suffices.

Rolling Circles answer explained:
Six circumference lengths of the larger disk are equal to seven circumference lengths of the smaller disk. This distance must be traveled before P and Q again coincide. This causes the smaller disk to execute 13 full rotations. Seven come from the rotations it would accumulate on a straight path and six come from traveling around the larger disk six times.

## Recent Weeks

Links to all of the puzzles and solutions are on the Complete Varsity Math page.

Come back next week for answers and more puzzles.