Question 8
x (m)
0
40
40
y (m)
0
0
30
A child starts moving at A, travels 40 m east to B, and then travels 30 m north to C. What is the total distance travelled, and the magnitude of the displacement?
The right answer is the one marked above.
Distance 70 m, displacement 50 m. The total distance is the sum of the two legs: 40 m + 30 m = 70 m.
The displacement is the straight-line distance from A to C. Since AB and BC are at right angles, Pythagoras gives AC: 40² + 30² = 1600 + 900 = 2500, so AC = 50 m. Its direction is from A towards C.
The two displacements are not along the same line, so they cannot simply be added here — 70 m is what you get by adding them as if they were.