Solving a Ski Slope: Length & Time for Descent

[HT3]

Homework Statement

A skier is gliding along at 3m/s on horizontal frictionless snow. He suddenly starts down a 10 degree incline. His speed at the bottom is 15 m/s.
a) what is the length of the incline?
b) how long does it take for him to reach the bottom?
we know:
Vo=3m/s
Vf=15m/s
t=?
x=?
a=?

Homework Equations

V^2=Vo^2 +2ax

The Attempt at a Solution

i need help to find what the a is...and why it is that.

 

[bob1182006]

the only force acting on the skier is gravity but since the skier is going down a 10 degree incline gravity is giving him some acceleration but not 100% of it's full foce.

draw the Free Body Diagram and split up gravity into it's components where the acceleration will be parallel to the incline.

 

[HT3]

okay from my freebody diagram i get sin(10)=9.8/a
a=56.4
and that is wrong...if anyone could explain to me how to do it properly please...id greatly appreciate it because i have my exam very soon.

 

[bob1182006]

it should be 9.8*sin(10). the force acting parallel to the inclined plane is mgsin(theta).