Two highways intersect as shown in the figure. At the instant shown, a police ca

Question

Two highways intersect as shown in the figure. At the instant shown, a police car P is distance dP = 770 m from the intersection and moving at speed vP = 77 km/h. Motorist M is distance dM = 400 m from the intersection and moving at speed vM = 40 km/h. What are the (a)x-component and (b)y-component of the velocity (both in km/h) of the motorist with respect to the police car? (c) For the instant shown in the figure, what is the angle between the velocity found in (a) and (b) and the line of sight between the two cars?

Explanation / Answer

Since the cars are travelling on the x & y axes, the x-y velocity components are just the car velocities. But the velocity of M with respect to P is Vm - Vp, so Vp is negated: Vx = -Vp = -78 km/h Vy = Vm = 56 km/h The resultant velocity angle ?v and line of sight angle ?s are: ?v = atan(Vm/(-Vp)) = -35.7° ?s = atan(dm/dp) = 35.7°

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