Toboggan down hill, FIND ANGLE?

[j_suder2]

Homework Statement

A girl starting from rest, toboggans down a hill of height 15m. The mass of the girl and toboggan is 42kg. The speed of the girl and toboggan at bottom of hill is 2.9m/s. If force of friction is 112 N, what is the slope of the hill? Ignore air resistance.

Homework Equations

KE=PE, 15sin(theta), F=mg

The Attempt at a Solution

I started by equating initial and final energies by saying KE final is equal to PE initial plus the force of friction. (.5mv)squared = mgh - (mu)Fn
I ended up with 0.1429=sin(theta) which equals 8.2 degrees. The answer was 16 degrees, where did I go wrong?

 

[kplooksafterme]

What is 15sin(\vartheta) meant to be?

 

[j_suder2]

I am trying to figure out the distance down the slope that she travels so I can use that along with the height (15m) to find the angle.

 

[kplooksafterme]

15sin(theta) will not give you the distance traveled down the slope.

 

[j_suder2]

Well I suppose I am stuck then.

 

[kplooksafterme]

You know what to do, you just have your trig relations mixed up a bit. If sintheta = height/hypotenuse, then 15sintheta = height x height/hypotenuse...

 

[j_suder2]

I should know this, but that still leaves me with unknowns for theta and hypotenuse.
I am drawing a blank on how to find the hypotenuse with what is given.
Thanks for the replies by the way.

 

[kplooksafterme]

Sintheta = height/hypotenuse where hypotenuse = the distance traveled down the slope. Since we know the height, we can state the hypotenuse in terms of the height and theta, that is hypotenuse = height/sintheta. This way you can use 15m/sintheta in the expression for the work done by friction, and then solve for theta, which was your idea to begin with. You just misused the sin ratio!

 

[Squeezebox]

W=Ff*d


5997.4/112N=d

d=53.6m

 

[j_suder2]

Beautiful. Thanks much!

 

[j_suder2]

So how did you determine W was 5997.4?

 

[Hootenanny]

I have to disagree with Squeezebox, the work done is not as quoted. To calculate the work done, you can apply conservation of energy.