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...

Question

ANS: tan-1(1/2)

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

Answer 1

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)