Conservation of energy of a skier

[brycenrg]

Homework Statement

A skier starts at the top of a friction less hill. You have 4 different runs, they have different difficulties. So I am assuming they are at different inclines. 1) longest route, not so steep 2) medium length, little steeper 3) shorter more steep 4) straight path, and very steep 5) all the same

On which run does her gravitational potential energy change the most?

On which run would her speed at the bottom be the fastest?

Which run would she get to the bottom the the quickest?

Homework Equations

Ei = Ef
mgh = 1/2mv^2

The Attempt at a Solution

Since Potential Energy = mgh
H is the same, I can assume. P converts into K
mgh = 1/2mv^2
so the final velocity will be the same for all. Kinetic energy is not a vector quantity either.
The gravitational potential energy will change the same amount in all runs.
The speed will be the same at the bottom for all runs.
She would get to the bottom the quickest at the steepest path. but would still have the same final energy or velocity/KE at the bottom.

Is this correct? for the longest time i thought they would get to the bottom at the same time but i don't think so anymore.
[/B]

 

[ehild]

Homework Statement

A skier starts at the top of a friction less hill. You have 4 different runs, they have different difficulties. So I am assuming they are at different inclines. 1) longest route, not so steep 2) medium length, little steeper 3) shorter more steep 4) straight path, and very steep 5) all the same

On which run does her gravitational potential energy change the most?

On which run would her speed at the bottom be the fastest?

Which run would she get to the bottom the the quickest?

Homework Equations

Ei = Ef
mgh = 1/2mv^2

The Attempt at a Solution

Since Potential Energy = mgh
H is the same, I can assume. P converts into K
mgh = 1/2mv^2
so the final velocity will be the same for all. Kinetic energy is not a vector quantity either.
The gravitational potential energy will change the same amount in all runs.
The speed will be the same at the bottom for all runs.[/B]

Correct so far...

She would get to the bottom the quickest at the steepest path. but would still have the same final energy or velocity/KE at the bottom.

Is this correct? for the longest time i thought they would get to the bottom at the same time but i don't think so anymore.

What does your last sentence mean?

The motion of the skier can be thought as the resultant of its vertical motion and its horizontal motion. The vertical displacement h is the same for all routes. The displacement is h = a/2 t². How does the vertical acceleration depend on the steepness of the slope?

 

[brycenrg]

What does your last sentence mean?

The motion of the skier can be thought as the resultant of its vertical motion and its horizontal motion. The vertical displacement h is the same for all routes. The displacement is h = a/2 t². How does the vertical acceleration depend on the steepness of the slope?[/QUOTE]

If I fell off of a height of H. The force of gravity is mg
Now if I fell off a slope with 80 decline. The force of gravity is only mg(cos(10)). Is this correct way in thinking?