Question

A horse runs along a circle with a speed of 20 km/hr . A lantern is at the centre of the circle. A fence is along the tangent to the circle at the point at which the horse starts . The speed with which the shadow of the horse moves along the fence at the moment when it covers 1/8 of the circle in km/hr is

• A. 20
• B. 40
• C. 30
• D. 60

Answer 1

Answer: (B)

$\tan \theta= x / r \Rightarrow x = r \tan \theta $
$\Rightarrow dx / dt = rsec \log ^2 \theta( d \theta / dt )= r \omega \sec ^2 \theta= v \sec ^2 \theta$
$\text { where } \theta=\pi / 8, dx / dt = v \sec ^2(\pi / 4)=2 v =40 km / hr ; \theta=45^{\circ}$