A skier is gliding along at 4.0 m/s on horizontal, frictionless snow. He suddenly starts down a 10 degree incline. His speed at the bottom is 16 m/s.What is the length of the incline? How long does it take him to reach the bottom?
When the skier enters the inclined zone due to his weight there will be a force acting on him which makes him accelerates down on the plane.
The acceleration of a component of gravitational acceleration along the incline plane.
Acceleration `a = gsin10` (which is shown in figure)
Using equation of motion;
`v^2 = u^2+2aS`
`16^2 = 4^2+2gsin10xxS`
`S = 70.44m`
Using `v = u+at`
`16 = 4+gsin10t`
`t = 7.044s`
So the length of slope is 70.44m and the time taken to complete the travel is 7.044 seconds.