1. Cars at equator
Imagine that there is a highway along the equator of the Earth. Two identical cars (with identical drivers) set off in opposite directions on this highway – one eastwards, and the other, westwards. Which car will wear its tires off first? Why?
This puzzle deals with physics. For an object that travels uniformly in a circular manner (uniform circular motion), it will experience a centrifugal force radically outwards. This force increases with the speed of the circular motion.
Hence the faster a body travels, the lesser it will weight (weight = gravitational contribution – centrifugal contribution).
The earth rotates from west to east. Hence the car moving eastwards, will be moving faster (relative motion around the centre of the earth) than the car westwards. This will make the car travelling eastwards lighter, and the car travelling westwards heavier. Since friction is proportional to the normal reaction (weight), the car travelling westwards will wear its tires off first.
You are inside a perfectly cubical room where each wall, the ceiling and the floor are mirrors. There is nothing else in the room. Assuming that you can still breathe, how many reflections can you see if you’re facing one direction, and can look up, down, left and right?
3. Crossing the Desert
An explorer named Marco wants to cross an Australian desert on foot. The track will begin in the outback at the aboriginal village of Kwazi and takes six days. However, one man can only take enough food to last him four days. Fortunately, Marco can hire porters from Kwazi to assist him. Each porter costs $100 per day that he is away from the village. What is the least possible cost to Marco of hiring enough porters so that he can cross the desert and the porters can return home safely? Explain your answer.
Day 0: Marco leaves with 2 porters
Day 1: Porter 1 goes back home and gives Porter 2 and Marco 1 pack each
Day 2: Porter 2 goes back home and gives Marco 1 pack
Day 3: Marco has 4 packs, and 4 days to go!