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**1. The problem statement, all variables and given/known data**

A child sits on a sled (50kg) on a snowy hill with an incline of 5 degrees. The coefficient of static friction is 0.05. What downward force must a parent apply parallel to the normal force, to prevent the child from sliding down the hill? (Answer: 366N)

**2. Relevant equations**

Ffs= MsFn

Ffs= MsFn

**3. The attempt at a solution**

I drew out the problem on an x-y axis.

Ffs(-x direction)

Fn(+y direction)

Fa(+x direction)

Fg(-y direction, x direction)

Fgx(-y, +x direction)

Fgy(-y direction)

Looks like this ^ when mapped out. I then separated equations based on both directions

Fg=Ma

Fg= 50kg⋅9.8m/s^2

Fg= 490N

__x direction__-Ffs+Fgx+fa=Ma,x

-Ffs+Fg(sinθ)= 0m/s^2

y directiony direction

Fn-Fgy=Ma,y

Fn-Fg(cosθ)= 0m/s^2

Fn= Fg(cosθ)

__Solving__- Fn= 490N(cos5)

- Ffs= .05(488N)

- -Ffs+fg(sinθ)+fa= 0m/s^2

Fa= 67N ...... What did i do wrong here?