Two highways intersect as shown in Fig. 4-55. At the instant shown, a police car

Question

Two highways intersect as shown in Fig. 4-55. At the instant shown, a police car P is 800 m from the intersection and moving at 40 km/h. Motorist M is 600 m from the intersection and moving at 30 km/h.

(a) In unit-vector notation, what is the velocity of the motorist with respect to the police car?
(40 ihat + -30 jhat) Correct!

(b) For the instant shown above, how does the direction of the velocity found in (a) compare to the line of sight between the two cars?
a)The velocity is at 60° to the line of sight.
b)The velocity is perpendicular to the line of sight.
c)The velocity is along the line of sight.
d)The velocity is at 45° to the line of sight

(c) If the cars maintain their velocities, do the answers to (a) and (b) change as the cars move nearer to the intersection?

Explanation / Answer

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. =-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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