Question

A 13 ft ladder is leaning against a wall. If the top of the

ladder slips down the wall at a rate of 2 ft/s, how fast will

the foot be moving away from the wall when the top is 5 ft

above the ground?

Answer 1

L=13

$\frac{dy}{dt}=2$

y=5

we are to find $\frac{dx}{dt}$ when $\frac{dy}{dt}=2$ and y=5

$x^2+y^2=13^2$ ......................(i)

$\therefore 2x\frac{dx}{dt}+2y\frac{dy}{dt}=0$ ............(ii)

from(i) $x=\sqrt{13^2-5^2}=12$

from (ii);

$2(12)\frac{dx}{dt}+2(5)(2)=0$

$\frac{dx}{dt}=-\frac{5}{6}$

$=-\frac{5}{6}ft/s$