Answer:
The velocity of the skier at the bottom of the ramp is approximately 26.288 meters per second.
Explanation:
We can determine the final velocity of the skier at the bottom of the ramp by Principle of Energy Conservation and Work-Energy Theorem, whose model is:
(1)
Where:
, - Initial and final gravitational potential energy, measured in joules.
, - Initial and final translational kinetic energy, measured in joules.
- Work dissipated by friction, measured in joules.
By definitions of gravitational potential and translational kinetic energy and work, we expand and simplify the model:
(2)
Where:
- Mass, measured in kilograms.
- Gravitational acceleration, measured in meters per square second.
, - Initial and final heights of the skier, measured in meters.
- Normal force from the incline on the skier, measured in newtons.
- Distance covered by the skier, measured in meters.
- Kinetic coefficient of friction, dimensionless.
The normal force exerted on the skier and the covered distance are, respectively:
(3)
(4)
Where is the angle of the incline above the horizontal, measured in sexagesimal degrees.
By applying (3) and (4) in (2), we get that:
(5)
Then, we clear the velocity of the skier at the bottom of the ramp is: (, , , , )
(6)
The velocity of the skier at the bottom of the ramp is approximately 26.288 meters per second.