Question

A particle moves over three of a circle of radius r. What is the magnitude of its displacement?

Answer 1

Imagine this problem as a clock,
The hour hand and the minute hand are at 12.
Let's imagine that the hour hand remains intact while the minute hand completes 3 quarters and reaches 9.
The angle between the hour hand and minute hand is 90° (for magnitude only).
So by applying Pythagoras theorem,
Displacement= √(r^2 + r^2))
Which comes out to be r√2.