A car travels 18 km / h to the northwest. What is the speed of this car seen from another car going south at 60 km / h?

73.8 km/h

Explanation:

The velocity of object A relative to object B is:

v = va − vb

Let's say east is +x and north is +y, and angles are measured from +x.

The velocity of the first car in the x direction is:

18 km/h cos 135° = -9√2 km/h

The velocity of the first car in the y direction is:

18 km/h sin 135° = 9√2 km/h

The velocity of the second car in the x direction is:

60 km/h cos 270° = 0 km/h

The velocity of the second car in the y direction is:

60 km/h sin 270° = -60 km/h

The relative velocity in the x direction is:

vₓ = -9√2 km/h − 0 km/h = -9√2 km/h ≈ -12.7 km/h

The relative velocity in the y direction is:

vᵧ = 9√2 km/h − (-60 km/h) = 9√2+60 km/h ≈ 72.7 km/h

The speed, or magnitude of the velocity, is:

v = √(vₓ² + vᵧ²)

v = √((-12.7 km/h)² + (72.7 km/h)²)

v ≈ 73.8 km/h

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