A skier is gliding along at 4.9m/s on horizontal, frictionless snow. He suddenly starts down a 10∘ incline. His speed at the bottom is 11m/s .

How long is the slope?
How long does it take to reach the bottom?

Think i would use
v^2_Final=V^2_initial X 2a(Change over x)

But not sure how to apply it?

This post was edited by Elements_Fury on Sep 10 2013 01:17pm

Heh your first incline plane problem? Your cherry is about to get popped.

In general you will want to draw pictures for these kinds of problems. Give me a min and I'll draw one for you.

This post was edited by Azrad on Sep 10 2013 01:22pm

Purple vector is the force of gravity.

This purple vector is essentially useless to us in its current form, so we decompose it into 2 vector, one directly into the ramp (which we will no longer need, but in future problems you will do involving friction we will need this vector so I have included it), and one vector down the ramp. These are the red vectors.

So the force on the person on the ramp from gravity, in the direction down the ramp is: m*g*cos(90-Ѳ)
FYI, cos(90-Ѳ) is generally written as sin(Ѳ)
So restarting the above: m*g*sin(Ѳ)
but we want their acceleration so....
F=ma
m*g*sin(Ѳ) = m*a
use g = 9.8 m/s^2 (this you just have to know, we are assuming this situation happened near the Earth, if your problem takes place on Mars you will have to look up this number).
use Ѳ = 10 (degrees, not radians!)
and m (the mass) will cancel so you don't need to know it (otherwise we would be totally boned, since the mass of the person was not given!).
You know everything except a so:
solve for a (acceleration), in m/s^2

now that you know the acceleration you can use the formula
Vf = a*t + Vi
Vf = velocity final (velocity at the bottom of the hill, given in the problem, in m/s)
Vi = velocity initial (velocity at the top of the hill, given in problem, in m/s)
t = time in seconds
You know everything except t (time), so solve for t. This is the answer to your second question

Now that you know t (time) you can use:
Pf = (1/2)*a*t^2 + Vi*t + Pi
Pi = Position initial, in meters, use 0
Pf = Position final, in meters, solve for Pf as you know all other values. This is the answer to your first question.

This post was edited by Azrad on Sep 10 2013 01:51pm