Answer:
Explanation:
Given
rope makes an angle of ![\theta](https://tex.z-dn.net/?f=%5Ctheta%20)
Mass of sled and snow is m
Normal Force ![=F_N](https://tex.z-dn.net/?f=%3DF_N)
applied Force is F
as Force is pulling in nature therefore normal reaction is given by
![F_N=mg-F\sin \theta](https://tex.z-dn.net/?f=F_N%3Dmg-F%5Csin%20%5Ctheta%20)
Also ![F\cos \theta =f_r](https://tex.z-dn.net/?f=F%5Ccos%20%5Ctheta%20%3Df_r)
![f_r=\mu _k\cdot F_N](https://tex.z-dn.net/?f=f_r%3D%5Cmu%20_k%5Ccdot%20F_N)
![f_r=\mu _k\cdot (mg-F\sin \theta )](https://tex.z-dn.net/?f=f_r%3D%5Cmu%20_k%5Ccdot%20%28mg-F%5Csin%20%5Ctheta%20%29)
-------1
---------2
Squaring 1 & 2 and then adding
![F^2=(\mu _kF_N)^2+(mg-F_N)^2](https://tex.z-dn.net/?f=F%5E2%3D%28%5Cmu%20_kF_N%29%5E2%2B%28mg-F_N%29%5E2)
![F=\sqrt{(\mu _kF_N)^2+(mg-F_N)^2}](https://tex.z-dn.net/?f=F%3D%5Csqrt%7B%28%5Cmu%20_kF_N%29%5E2%2B%28mg-F_N%29%5E2%7D)
Substitute value of F in 1
![cos\theta =\frac{\mu _KF_N}{\sqrt{(\mu _kF_N)^2+(mg-F_N)^2}}](https://tex.z-dn.net/?f=cos%5Ctheta%20%3D%5Cfrac%7B%5Cmu%20_KF_N%7D%7B%5Csqrt%7B%28%5Cmu%20_kF_N%29%5E2%2B%28mg-F_N%29%5E2%7D%7D)
![\theta =cos^{-1}(\frac{\mu _KF_N}{\sqrt{(\mu _kF_N)^2+(mg-F_N)^2}})](https://tex.z-dn.net/?f=%5Ctheta%20%3Dcos%5E%7B-1%7D%28%5Cfrac%7B%5Cmu%20_KF_N%7D%7B%5Csqrt%7B%28%5Cmu%20_kF_N%29%5E2%2B%28mg-F_N%29%5E2%7D%7D%29)
The Sun is 149.6 million kilometers from the earth.
There are 8760 hours in a year.
876000 km are traveled in a year
It would take 170.776 years to reach the sun, or 171 years rather
It would be A because it would make sense