9. Relative velocity in two dimensions

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4.9 Relative velocity in two dimensions

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The concept of relative velocity, introduced in section 3.7 for motion along a straight line, can be easily extended to include motion in a plane or in three dimensions. Suppose that two objects A and B are moving with velocities vA and vB (each with respect to some common frame of reference, say ground

.). Then, velocity of object A relative to that of B is :

vAB = vA – vB                                                         (4.35a)

and similarly, the velocity of object B relative to that of A is :

vBA = vB – vA NEETprep Audio Note (English):    

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Therefore, vAB = – vBA                                           (4.35b)

and,

(4.35c)

 

Example 4.6 Rain is falling vertically with a speed of 35 m s–1. A woman rides a bicycle with a speed of 12 m s–1 in east to west direction. What is the direction in which she should hold her umbrella ?

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Answer In Fig. 4.16 vr represents the velocity of rain and vb , the velocity of the bicycle, the woman is riding. Both these velocities are with respect to the ground. Since the woman is riding a bicycle, the velocity of rain as experienced by
Fig. 4.16
her is the velocity of rain relative to the velocity of the bicycle she is riding. That is vrb = vr– vb
This relative velocity vector as shown in Fig. 4.16 makes an angle θ with the vertical. It is given by
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Therefore, the woman should hold her umbrella at an angle of about 19° with the vertical towards the west.

Note carefully the difference between this Example and the Example 4.1. In Example 4.1, the boy experiences the resultant (vector sum) of two velocities while in this example, the woman experiences the velocity of rain relative to the bicycle (the vector difference of the two velocities).

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