The cliff divers of Acapulco push off horizontally from rock platforms about 35 m above the water, but they must clear rocky outcrops at water level that extend out into the water 5.0 m from the base of the cliff directly under their launch point. See Fig. 3-53. What minimum pushoff speed is neces- sary to clear the rocks? How long are they in the air? 35 m |5.0 m| FIGURE 3-53 Problem 64.

In Fig. 3-27, a heavy piece of machinery is raised by sliding it a distance d = 12.5 m along a plank oriented at angle θ = 20.0° to the horizontal. How far is it moved (a) vertically and (b) horizontally?

2-27. Derive the equation for the range of a projectile fired on level ground, u* sin 20 R where R is the range, 0 is the angle of elevation, and u is the initial velocity. Show that the maximum range is achieved when 0 = 45°.