Question

Two cars A and B are moving along on a straight line .Car A is moving at speed 80km/hr whole car B is moving at a speed 50km/hr in the same direction. Find the magnitude An d direction of 1)th e relative velocity of car A with respect to B 2)th e relative velocity of car B with respect to car A

Answer 1

a) relative velocity of car A with respect to B is
= 80 - 50
= 30 km/h.
here the direction of car A is along the line of motion of the car B as magnitude comes out to be +ve.

b) relative velocity of car B with respect to A is
= 50 - 80
= -30 km/h.
here direction of car B is opposite to the direction of car A as magnitude comes out to be -ve.
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Answer 2

For no collision the velocity of A must reduce to that of velocity of B.

VA = 30 m/s , VB = 20 m/s , a = - 2 m/s2

i.e. the relavitive final velocity of A with respect to B must be 0. Vr = 0

The relative initial velocity of A with respect to B is ( VA-VB )

The relative acceleration of A with respect to B is (-a - 0 ) = - a

Using the equation : v2= u2+ 2as

0 = ( VA-VB )2 + 2 × -a × s'

s' = ( VA-VB )2 / 2 a

= (30-20) 2 / 4

=25 m

Hence no collision occurs when d is greater than 25 m

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