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.

••• At time t = 0 a ball is thrown with speed v0 at an angle θ above a slope that is itself inclined at an angle ϕ above the horizontal (Fig. 1). (a) Choosing axes as shown, write down the components of the ball’s initial velocity v0 and its acceleration g. Hence find the ball’s position (x, y) as a function of time and show that its range up the slope is

Note that when the ball lands, y = 0. (b) Show that you gel the same final answer if you use axes Ox′ y′ with Ox′ horizontal and Oy′ vertical. Discuss briefly the merits of the two choices of axes. (You can find several useful trig identities in Appendix B.)

FIGURE 1