# Varsity Math, Week 123

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

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### 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.