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 = 820 m from the intersection and moving at speed vP = 82 km/h. Motorist M is distance dM = 540 m from the intersection and moving at speed vM = 54 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

with respect to police car, velocity of motorist:

= Vm - Vp

= -54j - (-82i)

= 82i - 54j

a) X component = 82 Km/hour

b) Y component = -54 Km/hour

c) angle with police car = 146.63 degree

angle with motorists = 56.63 degrees

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