Question

A cyclist moves around a circular path of radius $39.2\sqrt{3}$ metres with a speed of 19.6 $m{s}^{-1}$. He must lean inwards at an angle $\theta$ with the vertical such that $tan\theta$ is:

• A. $1$
• B. $\sqrt{3}$
• C. $\frac{1}{\sqrt{3}}$
• D. $2$

Answer 1

Answer: (C)

$\frac{1}{\sqrt{3}}$

$Ncos\theta =mg$
$Nsin\theta =\frac{m{v}^2}{r}$
$tan\theta =\frac{v^2}{rg}$
$=\frac{(19.6{)}^2}{39.2\sqrt{3}\times 9.8}$
$=\frac{1}{\sqrt{3}}$