Chapter 4, Problem 101RPP

Ski jumping in Vancouver The 2010 Olympic ski jumping competition was held at Whistler Mountain near Vancouver During a jump, a skier starts near the top of the in-run, the part down which the skier glides at increasing speed before the jump The Whistler in-run is 116 m long and for the first part is tilted down at about 35° below the horizontal. There is then a curve that transitions into a takeoff ramp, which is tilted 11° below the horizontal. The skier flies off this ramp at high speed body tilted forward and skis separated (Figure 4.15). This position exposes a large surface area to the air, which creates lift, extends the time of the jump, and allows the jumper to travel farther In addition, the skier pushes off the exit ramp of the in-run to get a vertical component of velocity when leaving the ramp. The skier lands 125 m or more from the end of the in-run The landing surface has a complex shape and is tilted down at about $35°$ below the horizontal The skier moves surprisingly close (2 to 6 m) above the snowy surface for most of the jump The coefficient of kinetic friction between the skis and the snow on the in-run is about $0.05\pm 0.02$, and skiers’ masses are normally small—about 60 kg. We can make some rough estimates about an idealized ski jump with an average in-run inclination of $\left(35°+11°\right)/2=23°$.

Which answers below are closest to the magnitude of the skier's acceleration while moving down the idealized in-run and to the skier's speed when leaving its end?

$\begin{array}{l}\text{a}\text{. 9}{\text{.8 m/s}}^{\text{2}}\text{, 48 m/s}\hfill \\ \text{b}\text{. 4}{\text{.3 m/s}}^{\text{2}}\text{, 32 m/s}\hfill \\ \text{c}\text{. 4}{\text{.3 m/s}}^{\text{2}}\text{, 28 m/s}\hfill \\ \text{d}\text{. 3}{\text{.4 m/s}}^{\text{2}}\text{, 32 m/s}\hfill \\ \text{e}\text{. 3}{\text{.4 m/s}}^{\text{2}}\text{, 28 m/s}\hfill \end{array}$