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A cyclist in an Olympic race is moving in a circular track of radius 80 m with speed 72 km/h. He has to lean from the vertical approximately through an angle of...
ANS: tan-1(1/2)

How is tan-1(1/2) derived in this answer?

  • physics -

    draw a sketch of the cyclist.

    notice from her center of gravity, a horizontal force (centripetal force) of mv^2/r
    the vertical force is mg

    so tan Theta= mv^2/mgr=v^2/gr

    now, the numbers v=72km/hr=20m/s (how convenient ) , and r=80
    tanTheta=20^2/9.8*80=.51
    theta=arctan(.51)

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