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 move along the fence at the moment when it covers $\frac{1}{8}$ of the circle in km/hr is

• A. 20
• B. 40
• C. 30
• D. 60

Answer 1

The correct option is B

40

$tan\theta =\frac{x}{r}\Rightarrow x=rtan\theta$

$\Rightarrow \frac{dx}{dt}=rse{c}^2\theta \left(\frac{d\theta }{dt}\right)=r\omega se{c}^2\theta =vse{c}^2\theta where\theta =\frac{\pi }{8},\frac{dx}{dt}=vse{c}^2\left(\frac{\pi }{4}\right)=2v=40km/hr;‘\theta ={45}^{\circ }$
Hence the correct option is b