Two highways intersect a police car P is distance dP =800 m from the intersectio

Question

Two highways intersect a police car P is distance dP =800 m from the intersection and moving east at speed vP = 80 km/h. Motorist M is distance dM = 600 m from the intersection and moving south at speed vM = 60 km/h. (a)in unit vector notation, what is the velocity of the motorist with respect to the police car?(b) 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 answers to (a) and (b) change as the cars move nearer the intersection an WHY?

Explanation / Answer

follow this a) velocity of the motorist w.r.t velocity of the police car is v = vmotor - vpolice =-30 j^-(-40 i^) = (40 i^ - 30 j^) km/h ? = tan-1(-30/40) = -36.86 deg b) position vector d = 800 i^-600j^ ? = tan-1(-600/800) = -36.86 deg therefore, these two ate in same direction.so the angle between them is zero. c) (a) and (b) answers does not change.

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