Physics 5054/12 — October/November 2021

Walkthrough

Displacement is a vector quantity that measures the straight-line distance from the starting point to the final position, along with the direction. For the overall displacement to be zero, the boy's final position must be exactly the same as his starting point P. Therefore, he must walk from R back to P.

The shortest distance between any two points is a straight line, so we need to find the length of the straight line PR. The boy's path from P to Q to R forms two legs of a right-angled triangle: 3.0 m due north and 4.0 m due east. Since north and east are perpendicular, we can apply Pythagoras' theorem to find the hypotenuse PR:

$$PR = \sqrt{PQ^2 + QR^2}$$ $$PR = \sqrt{3.0^2 + 4.0^2} = \sqrt{9.0 + 16.0} = \sqrt{25.0} = 5.0 \text{ m}$$

This matches option C.

Key Takeaways

• Displacement is a vector; zero overall displacement means returning to the starting point.
• The shortest distance between two points is a straight line.
• Pythagoras' theorem ($a^2 + b^2 = c^2$) is used to find the resultant of two perpendicular vectors.

Common Mistakes

• Adding the distances: Choosing 7.0 m (option D) by simply adding 3.0 m and 4.0 m. This calculates the total distance walked, not the displacement.
• Confusing distance and displacement: Forgetting that displacement is a vector quantity that depends only on the start and end points.

Things to Be Careful About

• Always distinguish between distance (a scalar, total path length) and displacement (a vector, straight-line change in position).
• When combining perpendicular vectors, use Pythagoras' theorem for the magnitude and trigonometry for the direction. Here, only the magnitude (distance to walk) is required.