Answer
The required time is $8.2s$
Work Step by Step
1) Find the acceleration $a$ of the girl
- The weight of the girl and the sled is manifest in the form $Mg\sin30=65\times9.8\sin30=318.5N$, which pushes them downward.
- The wind also pushes them downward with $F=105N$
- Kinetic friction opposes the motion: $f_k=\mu_kF_N=\mu_kMg\cos30=0.15(65\times9.8\cos30)=82.75N$
(Normal force $F_N$ here is equal with the vertical component of the weight of the girl and the sled, which is $Mg\cos30$)
Newton's 2nd Law: $$Mg\sin30+F-f_k=Ma$$ $$a=\frac{Mg\sin30+F-f_k}{M}=5.24m/s^2$$
2) Find $t$
We have $a=5.24m/s^2$, $v_0=0$ and slope length $x=175m$
$$x=v_0t+1/2at^2=1/2at^2$$ $$t=8.2s$$
