Halliday, Resnick & Walker — Motion in Two and Three Dimensions: Problem 73

Two highways intersect as shown in Fig. 4.26. At the instant shown, a police car $P$ is distance $d_P = 800\text{ m}$ from the intersection and moving at speed $v_P = 80\text{ km/h}$. Motorist $M$ is distance $d_M = 600\text{ m}$ from the intersection and moving at speed $v_M = 60\text{ km/h}$. (a) In unit-vector notation, what is the velocity of the motorist with respect to the police car? (b) For the instant shown in Fig. 4.26, what is the angle between the velocity found in (a) and the line of sight between the two cars? (c) If the cars maintain their velocities, do the answers to (a) and (b) change as the cars move nearer the intersection?