A cyclist while negotiating a circular path with speed `20 ms^(-1)` is found to bend an angle by `30^(@)` with vertical. What is the radius of the circular path? (given,`g=10 ms^(-2))`.

Explanation

Speed of the cyclist, `v =20 ras^(-1)`
Angle of bending with vertical,`theta=30^(@)`
Equation for angle of bending, `tan theta=(v^(2))/(rg)`
Rewriting the above equation for radius `r=(v^(2))/(tan theta g)`
`r=((20)^(2))/((tan 30^(@))xx10)=(20xx20)/((tan 30^(@))xx10)=(400)/(((1)/(sqrt(3)))xx100)`
`r=(sqrt(3))xx40=1.732xx40`
`r=69.28m`