Question

A boy is moving along a circular track in an anticlockwise sense. A girl moves along a regular hexagonal path. The centres of hexagonal track and a circular track coincide as shown in the figure. The girl and the boy starts from point B and A such that P, A & B always lie on the same radial line. The velocity of the boy is 1m/s. Given side length of regular hexagon is "a" and radius of circular path is $\frac{a}{\sqrt{3}}$. The speed of Girl at point C is___

Answer 1

$tan\theta =\frac{2x}{a\sqrt{3}}$

$x=\frac{a\sqrt{3}}{2}tan\theta$

$\frac{dx}{dt}=\frac{a\sqrt{3}}{2}se{c}^2\theta \frac{d\theta }{dt}=v_{girl}$;

$\frac{d\theta }{dt}=\omega =\frac{v_{boy}}{\frac{a}{\sqrt{3}}}=\frac{1\sqrt{3}}{a}$

$v_{girl}=2m/sat\theta ={30}^{\circ }$