Please show all work and equations: Two highways intersect as shown in the figur

Question

Please show all work and equations:

Two highways intersect as shown in the figure. At the instant shown, a police car P is distance dP = 750 m from the intersection and moving at speed vP = 75 km/h. Motorist M is distance dM = 580 m from the intersection and moving at speed vM = 58 km/h. What are the (a) x-component and (b) y-component of the velocity 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? Number Units Number Units Number Units

Explanation / Answer

a) Vmp = Vm - Vp   = -58 j - (-75)i = 75i - 58j

a   = 75 km/h

b) - 58 km/h

c) sight of cars angle = tan-1(580/750) = 37.72 degrees

angleof v = tan-1(58/75) = - 37.72 degrees.

angle =2 x 37.72 = 75.43 degrees

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