Help with Newtons laws and friction

[beamerrox]

Homework Statement

a girl is skiing down a 35 degree inclined hill that is 120 meters long. She starts from rest and the snow has a coefficient of friction of .12.
A. Draw an FBD
B what is her acceleration
c. How much time dows it take her to travel the 120 meters

Homework Equations

I am unsure on how to set up the question solution. I think it's CAE's that are used as well, but i am completely unsure.

The Attempt at a Solution

ΣF= MA
ΣF=9.8(m)
vi= 0m/s
ΛD=120 m
vf = ?
t=?
a=?
120cos35= 98.29?
120sin35= 68.82?

If anyone could please help i would really appreciate it. If i can figure out how to set this problem up and solve it, i will be able to figure the other problems out. Thank you so much!
I don't think there's enough to solve it using cae's can i use the sin and cosine functions with the 35 degrees??

 

[Hannisch]

You have to take her direction of motion into consideration. If you've drawn a FBD you see that there's a difference in the direction of the forces that have an effect on her acceleration. If you can take this into consideration?

 

[thomate1]

Hello! I would be happy to assist you with understanding Newton's laws and friction. Let's start by drawing a free body diagram (FBD) for the girl skiing down the hill. An FBD is a visual representation of all the forces acting on an object. In this case, the object is the girl.

A. FBD:
The girl is represented as a dot in the middle of the diagram. The forces acting on her are the gravitational force (Fg), the normal force (Fn), and the frictional force (Ff). The gravitational force is pointing straight down, the normal force is perpendicular to the surface of the hill, and the frictional force is pointing up the hill.

B. Acceleration:
To find the girl's acceleration, we can use Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (ΣF=MA). Since we know the mass of the girl (let's say it's 50 kg), we can solve for the acceleration by dividing the net force by her mass.

To find the net force, we need to first find the components of the gravitational force and the frictional force. We can use trigonometry to do this. The component of the gravitational force acting down the hill is Fgcos35, and the component acting perpendicular to the hill is Fgsin35. The frictional force is equal to the coefficient of friction (μ) multiplied by the normal force (Fn).

So our equation for the net force is:
ΣF = Fgcos35 - μFn

Substituting in the values we know, we get:
ΣF = (50 kg)(9.8 m/s^2)cos35 - (0.12)(Fn)

To find the normal force, we can use Newton's third law, which states that for every action, there is an equal and opposite reaction. In this case, the normal force is equal to the component of the gravitational force perpendicular to the hill, or Fgsin35.

So our equation for the normal force is:
Fn = Fgsin35

Substituting in the values we know, we get:
Fn = (50 kg)(9.8 m/s^2)sin35

Now we can substitute this value into our equation for the net force:
Σ