To determine the relative velocity of two objects, we need to find the vector sum of their velocities. In this case, we have Car A moving north at 40 km/h and Car B moving west at 60 km/h.
Let's represent the velocity of Car A as vA and the velocity of Car B as vB.
vA = 40 km/h north vB = 60 km/h west
To find the relative velocity, we need to combine the two velocities vectorially. Since they are moving in perpendicular directions, we can use the Pythagorean theorem to find the magnitude of the resultant velocity, and then use trigonometry to determine the direction.
The magnitude of the resultant velocity (vR) can be calculated as:
vR = sqrt(vA^2 + vB^2)
vR = sqrt((40 km/h)^2 + (60 km/h)^2)
vR = sqrt(1600 km^2/h^2 + 3600 km^2/h^2)
vR = sqrt(5200 km^2/h^2)
vR ≈ 72.11 km/h
The direction of the resultant velocity can be determined using trigonometry. We can find the angle (θ) between the resultant velocity vector and the north direction by taking the inverse tangent of the ratio of the magnitudes of the north and west components:
θ = arctan(vA / vB)
θ = arctan(40 km/h / 60 km/h)
θ ≈ arctan(0.6667)
θ ≈ 33.69 degrees
Therefore, the velocity of Car A relative to Car B is approximately 72.11 km/h in a direction 33.69 degrees north of west. Similarly, the velocity of Car B relative to Car A is also 72.11 km/h, but in a direction 33.69 degrees south of east.