How can I calculate kinetic friction?

[Rick devena]

Homework Statement

A child slides down a slide with a 28 degree incline , and at the bottom her speed is precisly half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.

Homework Equations

Newtons second law

The Attempt at a Solution

https://www.physicsforums.com/attac...6/?temp_hash=7d75ca4df687186214dd365d2dd18568[/B]

 

[Simon Bridge]

I don't understand your writing ... I kinda see a diagram showing some forces, but I don't see a friction force on it, unless that's the "F" pointing down the slide.
There's something that looks like script-written "Als" ... maybe a scribbled $\mu_s$ or something ... cannot tell.
Please explain your reasoning.

 

[haruspex]

There are several things wrong with your equations.
If mg is the gravitational force and the slope is θ, what is the normal force, and what is the downslope component of gravity?