Relative Motion

In Section 1, “Velocity and Acceleration” the motion considered is relative to that of the earth which is assumed to be fixed. The Section on Relative Motion deals with problems involving relative motion. (Assume that the dimensions and masses of the bodies can be ignored i.e. they are treated as particles or points).

For example, two cars, A and B, are travelling in the same direction with velocities of 20 m/s and 25 m/s respectively, relative to the earth. However, the velocity of B relative to A is 25 ?20 = 5 m/s

Sample Problem: Cars crossing at an intersection

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?


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:

vA = 0 i + 20 j

vB = 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) = vB vA = (25 i + 0 j) ?(0 i + 20 j)

= (25 – 0) i – (0 + 20) j

= 25 i ?20 j

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