Question

A ladder 10 m long rests on horizontal ground and leans against a
vertical wall. The foot of the ladder is pulled away from the wall at 2
m/s. How fast is the top sliding down the wall when the foot of the
ladder is 6m from the wall?

Answer 1

x^2 + y^2 = 100 , where x is the base, y the height

2x dx/dt + 2y dy/dt = 0

given: dx/dt = 2 , and x = 6
then 36+y^2 = 100
y^2 = 64
y = 8

in
2x dx/dt + 2y dy/dt = 0
2(6)(2) + 2(8)dy/dt = 0
dy/dt = -24/16 = -3/2

it is sliding down at 3/2 m/sec

Answer 2

Let x represent the length of the ladder =10meters+5meters=x =x=10m+5m =15m :the length of the ladder is 10m