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## Homework Statement

I am worried that I don't understand a basic part of figuring out the component forces in the following problem. I have a full worked example but there is a few steps which I don't understand why we use sin for the x component and not cos (understand why I am really worried as it appears to be basic trig :/)

A 58-kg skier is coasting down a 25° slope, as Figure 6.7a shows. Near the top of the slope, her speed is 3.6 m/s. She accelerates down the slope because of the gravitational force, even though a kinetic frictional force of magnitude 71 N opposes her motion. Ignoring air resistance, determine the speed at a point that is displaced 57 m downhill.

## Homework Equations

vf = √2(KE

_{f}) / m

= √(2(1/2 mv

_{0}

^{2}+ Sigma F cos theta s)/m

= √(2(1/2 mv

_{0}

^{2}+ mg sin 25 - fk s) /m

= √(2(1/2 mv

_{0}

^{2}+ 170N cos 0 x 57) / 58

= 19m/s

## The Attempt at a Solution

This was in my textbook:

*a free-body diagram for the skier and shows the three external forces acting on her: the gravitational force , the kinetic frictional force , and the normal force . The net external force along the y axis is zero, because there is no acceleration in that direction (the normal force balances the component mg cos 25° of the weight perpendicular to the slope). Using the data from the table of knowns and unknowns, we find that the net external force along the x axis is:*

SigmaF = mg sin 25 - f

= (58)(9.8)(sin 25)(71)

= 170N

SigmaF = mg sin 25 - f

_{k}= (58)(9.8)(sin 25)(71)

= 170N

I look at sin and think we are looking at y component. I can't see why we would used sin for x component - can someone explain?

Many thanks

H

x

ps. please forgive formating - each time I use latex it just puts large gaps in the place of symbols :)