Question

A ladder $5m$ long is leaning against a wall. The foot of the ladder is pulled out along the ground away from the wall at a rate of $2m/s$. How fast is the height of ladder on the wall decreasing at the instant when the foot of the ladder is $4m$ away from the wall?

• A. $10m/s$
• B. $\frac{3}{2}m/s$
• C. $\frac{8}{3}m/s$
• D. $\frac{1}{10}m/s$

Answer 1

The correct option is C $\frac{8}{3}m/s$

At any instant $x^2+y^2=5^2$

Differentiating w.r.t. time $2x\frac{dx}{dt}+2y\frac{dy}{dt}=0$

When $x=4;y=3$

Here $\frac{dx}{dt}=2,\frac{dy}{dt}=u\Rightarrow u=\frac{8}{3}m/s$