Problems are listed in approximate order of difficulty. A single dot (•) indicates straigh...

Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.

•• A policeman is chasing a robber. Both are in cars traveling at speed v and the distance between them is l. The policeman wishes to shoot the robber with a gun whose muzzle velocity is u0. At what angle θ above the horizontal should he point his gun? First solve this problem using coordinates traveling with the policeman, as shown in Fig. 1. Then sketch the solution using coordinates fixed to the ground; is the angle of the gun the same as the angle of the bullet’s initial velocity in this frame? (The advantages of the first frame are not overwhelming; nevertheless, it is clearly the natural choice for the problem.)

FIGURE 1