Varsity Math, Week 123

Varsity Math 123

________________

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

________________

Miner

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

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?

momathlogohorizontalWSJLogo

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 120: Breakfast, Lunch, or Dinner? & The 2018 Puzzle, solutions to Solar Cap Versus Polar Cap & How Tall is the Pole

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.