**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*?

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**
*

**
**