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...

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?

Asked on by mango10

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

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.

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