Kinematics 6 Question 11
11. 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…… $m / s$.
(1987, 2M)
Show Answer
Answer:
Correct Answer: 11. 0.6
Solution:
- $\frac{x}{3}=\tan \theta$
$$ \therefore x=3 \tan \theta $$
$-\frac{d x}{d t}=3 \sec ^{2} \theta-\frac{d \theta}{d t}$
$$ -\frac{d x}{d t}=v _P \text { and } $$
$$ -\frac{d \theta}{d t}=\omega=0.1 rad / s, \theta=45^{\circ} $$
Substituting the values, we get
$$ v _P=3\left(\sec ^{2} 45^{\circ}\right)(0.1)=0.6 m / s $$
