## ________________

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?*

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## 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

**Week 122**: Minimum Racket Wear & Rolling Circles, solutions to Tennis Exhibition & Losing Streak

**Week 121**: Tennis Exhibition & Losing Streak, solutions to Breakfast, Lunch, or Dinner? & The 2018 Puzzle

**Week 119**: Solar Cap Versus Polar Cap & How Tall is the Pole, solutions to Relations Puzzle & Square Purchases

**Week 118**: Relations Puzzle & Square Purchases, solutions to Fifty-Fifty & Random Toss

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

**Come back next week** for answers and more puzzles.