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29 December, 23:38

Sam, whose mass is 75 kg, straps on his skis and starts down a 50-m-high, 20 frictionless slope. A strong headwind exerts a horizontal force of 200 N on him as he skies. Use work and energy to find Sam's speed at the bottom.

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  1. 30 December, 00:00
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    Sam mass=75kg

    Height is 50m

    20° frictionless slope

    Horizontal force on Sam is 200N

    According to the work energy theorem, the net work done on Sam will be equal to his change in kinetic energy.

    Therefore

    Wg - Ww = ∆K. E

    Note initial the body was at rest at top of the slope.

    Then, ∆K. E is K. E (final) - K. E (initial)

    K. E Is given as ½mv²

    Since initial velocity is zero then, K. E (initial) is zero

    Therefore, ∆K. E=½mVf²

    Wg is work done by gravity and it is given by using P. E formulas

    Wg=mgh

    Wg=75*9.8*50

    Wg=36750J

    Ww is work done by wind and it's is given by using formulae for work

    Work=force * distance

    Ww=horizontal force * horizontal distance

    Using Trig.

    TanX=opposite/adjacent

    Tan20=h/x

    x=h/tan20

    x=50/tan20

    x=137.37m

    Then,

    Ww=F*x

    Ww=200*137.37

    We=27474J

    Now applying the formula

    Wg - Ww = ∆K. E

    36750 - 27474 = ½*75*Vf²

    9276=37.5Vf²

    Vf²=9275/37.5

    Vf² = 247.36

    Vf=√247.36

    Vf=15.73m/s
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