RELATIVE MOTION PROBLEM WITH SOLUTION

Problem :Two cars are approaching an intersection. Car A is travelling north at 20 m/s while car B is travelling east at 25 m/s. What is the velocity of B relative to A?

Solution

The physical model of the intersecting car problem outlined above is illustrated in Fig. 1.

Let the velocities of cars A and B be represented by the following vectors:

v_A = 0 i + 20 j

v_B = 25 i + 0 j

The velocities of the cars are illustrated in Fig. 2 to provide a visual understanding of the problem:

The velocity of B relative to A (See also Fig. 2) = v_B - v_A = (25 i + 0 j) ?(0 i + 20 j)

= (25 - 0) i - (0 + 20) j

= 25 i ?20 j