Question

An 80 kg snowboarder is riding a half-pipe that is 15 m deep. If she begins at rest, how fast will she be traveling if there is no friction when she is 5 m from the bottom of the pipe?

Answer 1

The snowboarder will be traveling at a speed of approximately 17.1 m/s.

Step-by-step explanation:

To find the speed of the snowboarder, we can use the principle of conservation of energy. At the top of the half-pipe, the snowboarder will have potential energy due to her height and kinetic energy due to her motion. At the bottom of the pipe, she will have potential energy of zero and all her initial potential energy will have been converted into kinetic energy. We can equate these two energies to find her speed at the bottom:

mgh = (1/2)mv^2

where m is the mass of the snowboarder, g is the acceleration due to gravity, h is the depth of the half-pipe, and v is the speed of the snowboarder:

v = sqrt(2gh)

Plugging in the values given: m = 80 kg, g = 9.8 m/s^2, and h = 15 m, we can calculate the speed:

v = sqrt(2 * 9.8 * 15)

= sqrt(294)

≈ 17.1 m/s