Question #2044

Lori, who loves to ski, has rigged up a rope tow to pull herself up a local hill that is inclined at an angle of 30.0 degrees from the horizontal. The motor works against a retarding frictional force of 100 N. If Lori has a mass of 68.5 kg, and the power of the motor is 1350 W, at what speed can the motor pull her up the hill? Please answer in meters per second (m/s).

Expert's answer

<img src="/cgi-bin/mimetex.cgi?F%20=%20F_%7Bfrict%7D+%20F_%7Bweight%7D%20=%20100[N]%20+%2068.5[kg]10[N/kg]%20%5Csin%7B30%7D%20=%20442.5[N]" title="F = F_{frict}+ F_{weight} = 100[N] + 68.5[kg]10[N/kg] \sin{30} = 442.5[N]">

As <img src="/cgi-bin/mimetex.cgi?W%20=%20Fv" title="W = Fv">,

<img src="http://latex.codecogs.com/gif.latex?v%20=%20W/F%20=%201350%20/442.5%20=%203.05%20%5Cfrac%7Bm%7D%7Bs%7D" title="v = W/F = 1350 /442.5 = 3.05 \frac{m}{s}">

As <img src="/cgi-bin/mimetex.cgi?W%20=%20Fv" title="W = Fv">,

<img src="http://latex.codecogs.com/gif.latex?v%20=%20W/F%20=%201350%20/442.5%20=%203.05%20%5Cfrac%7Bm%7D%7Bs%7D" title="v = W/F = 1350 /442.5 = 3.05 \frac{m}{s}">

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