Question 6.12: The snowboarder A snowboarder starts from rest and descends ...
The snowboarder
A snowboarder starts from rest and descends a slope, losing 320 m of altitude in the process. What is her speed at the bottom? [Neglect all forms of resistance and take g=10 m s ^{-2}.]
The snowboarder moves under uniform gravity and the reaction force of the smooth hillside. Since this reaction force does no work, energy conservation applies in the form
\frac{1}{2} m| v |^{2}+m g z=E,
where m and v are the mass and velocity of the snowboarder, and z is the altitude of the snowboarder relative to the bottom of the hill. If the snowboarder starts from rest at altitude h, then E = 0 + mgh. Hence, at the bottom of the hill where z = 0, her speed is
| v |=(2 g h)^{1 / 2},
just as if she had fallen down a vertical hole! This speed evaluates to 80 ms ^{-1} , about 180 mph. [At such speeds, air resistance would have an important influence.]