Question

Spotlight S rotates in a horizontal plane with constant
angular velocity of 0.1 rad/s. The spot of light P moves
along the wall at a distance of 3 m. The velocity of the spot P
when $\theta$ = 45${}^{\circ }$ (see fig.) is.......m/s.

Answer 1

$\frac{x}{3}=tan\theta$
$\therefore x==3tan\theta$
$-\left(\frac{dx}{dt}\right)=3se{c}^2\theta (-\frac{d\theta }{dt})$
$-\frac{dx}{dt}=v_{p}and$
$-\frac{d\theta }{dt}=\omega =0.1rad/s.\theta =45^{\circ }$
Substituting the values, we get
$v_p=3(se{c}^{2}45^{\circ })(0.1)=0.6m/s$