Two bodies A and B are moving with velocities vec(V)_(A) and vec(V)_(B)making an'theta'with each other. Determine the relative velocity of Awith respect to B. What will be the relative velocity .When two bodies are moving inthe same direction.

Two bodies A and B are moving with velocities vec(V)_(A) and vec(V)_(B

1.	Two bodies A and B are moving with velocities vec(V)_(A) and vec(V)_(B)making an'theta'with each other. Determine the relative velocity of Awith respect to B. What will be the relative velocity .When two bodies are moving inthe same direction.
Answer» Solution :Let us CONSIDER the VELOCITIES `vec(V)_(A) and vec(B)`at an angle `theta`between their DIRECTIONS. The relative velocity of A with respect to B,`vec(v) _(AB) = vec(v)_(A) - vec(B)` . Then , the magnitude and direction of . `vec(V)_(AB)`is GIVEN by`v_(AB) = sqrt(v_(A)^(2) + v_(B)^(2) - 2v_(A) v_(B) cos theta)`and tan `beta = (v_(B) sin theta)/(v_(A) - v_(B) cos theta)`(Here `beta`is angle between `vec(v)_(AB) and vec(v)_(B)` ) . When `theta = 0`, the bodies move along parallel straight lines in the same direction. We have `v_(AB) = (v_(A) - v_(B))`in the direction of `vec(v)_(A)`. Obviously`v_(AB) = (v_(B) - v_(A))`in the direction of `vec(v)_(B)` .