Halliday, Resnick & Walker — Motion in Two and Three Dimensions: Problem 51

A skilled skier knows to jump upward before reaching a downward slope. Consider a jump in which the launch speed is \( v_0 = 10\text{ m/s} \), the launch angle is \( \theta_0 = 11.3^\circ \), the initial course is approximately flat, and the steeper track has a slope of \( 9.0^\circ \). Figure 4.22a shows a prejump that allows the skier to land on the top portion of the steeper track. Figure 4.22b shows a jump at the edge of the steeper track. In Fig. 4.22a, the skier lands at approximately the launch level. (a) In the landing, what is the angle \( \phi \) between the skier’s path and the slope? In Fig. 4.22b, (b) how far below the launch level does the skier land and (c) what is \( \phi \)? (The greater fall and greater \( \phi \) can result in loss of control in the landing.)