Question

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

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

Answer 1

Answer: (B)

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