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

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 4-33a shows a prejump that allows the skier to land on the top portion of the steeper track. Figure 4-33b shows a jump at the edge of the steeper track. In Fig. 4-33a, 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. 4-33b, (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.)