Question

A ladder $10metres$ long rests with one end against a vertical wall, the other on the floor. The lower end moves away from the wall at the rate of $2metres/minute$. The rate at which the upper end falls when its base is $6metres$ away from the wall

• A. $3metres/min$
• B. $2/3metres/min$
• C. $3/2metres/min$
• D. none of these

Answer 1

The correct option is C $3/2metres/min$

Given $\frac{dx}{dt}=2m/min$

We have, $x^2+y^2=100$

Also, when $x=6m\Rightarrow y=8m$

$2x\frac{dx}{dt}+2y\frac{dy}{dt}=0$

$\Rightarrow \frac{dy}{dt}=-\frac{3}{2}m/minute$