two highways intersecr at the instant. A police car P is 800 m from the intersec

Question

two highways intersecr at the instant. A police car P is 800 m from the intersection and moving at 80 km/h. Motorist M is 600 m from the intersection and moving at 60 km/h. (a) In unit-vector notarion. what is the velocity of the motorist with respect to the police car? (b) For the instant how does the direction of the velocity found in (a) compare to the line of sight between the two cars?(c) If the cars maintain their velocities, do the answer to (a) and (b) change as the cars move neaner the intersction?

Explanation / Answer

a) consider motorist moving towards +ve x direction and police towards +ve y direction....

velocity of motorist with respect to police will be 60i - 80j

b) angle of velocity of motorist with respect to police at that instant will be tan inverse(600/800) = tan inverse(6/8)

c) velocity doesn't depend on time in this case. So, (a) will not change..

but (b) depends on the distance..So, this changes as the cars move nearer.

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