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 = 890 m from the intersection and moving at speed vP = 89 km/h. Motorist M is distance dM = 560 m from the intersection and moving at speed vM = 56 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?

Explanation / Answer

a) apply relative in same direction = differnec of speeds

so Vmp = Vm - Vp

V = -56 j - (-89)i

V = 89i - 56j

Vx = 89

a) X component of speed Vx = 89 km/h

b.) Y component of speed Vy = 56 kmph

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c) sight of cars angle = tan-1(560/890)

tan theta = 0.629

theta =   32.17 deg

angleof v = tan-1(56/89) = - 32.17 degrees.

angle = 2 x 37.72 = 64.35 degrees

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