Question

A $13\, ft$. ladder is leaning against a wall when its base starts to slide away. At the instant when the base is $12\, ft$. away from the wall, the base is moving away from the wall at the rate of $5\, ft / sec$. The rate at which the angle $\theta$ between the ladder and the ground is changing is

• A. $-\frac{12}{13}\,rad / \sec$.
• B. $-1 \,rad / \sec$.
• C. $-\frac{13}{12} \,rad / \sec$.
• D. $-\frac{10}{13} \,rad / \sec$.

Answer 1

Answer: (B)

Where $x =12, \frac{ dx }{ dt }=5^{\prime} / sec$
$\frac{ d \theta}{ dt }=? $
$x =l \cos \theta $
$\frac{ dx }{ dt }=-l \sin \theta \frac{ d \theta}{ dt }$
$5=-13 \cdot \frac{5}{13} \frac{ d \theta}{ dt } $
$\Rightarrow \frac{ d \theta}{ dt }=-1 rad / sec \Rightarrow( B )$