Physics question about displacement?

Question

A car travels for 85 km due south for 2 hours. Then it travels 40 km due west for 1 hour. Finally, at travels 75 km at 30° south of west for 0.5 hours. What is the displacement?

Answer 1

Totalling components E and N:

E: - 40 - 75 cos(30) = - 104.95 km

N: - 85 - 75 sin(30) = - 122.50 km.

The displacement is 104.95 km W and 122.50 km S.

If you combine these as vectors, the magnitude of the displacement is:

sqrt(104.95^2 + 122.50^2)

= 161 km.

Its direction is theta south of west where:

tan(theta) = 122.50 / 104.95

theta = 49.4 deg.