Answer:
73.8 km/h
Step-by-step 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