The top of a ladder slides down a vertical wall at a rate of 0.125 m/s. At the moment when the bottom of the ladder is 5 m from the wall, it slides away from the wall at a rate of 0.3 m/s. How long is the ladder?

Question

anonymous · Answer

Ok so I know that I have to set it up as 2x(dx/dt)+2y(dy/dt)=2z(dz/dt)

anonymous · Answer

But how do I find z with just the information given?

perl · Answer

correct so far

perl · Answer

you can use pyth. theorem
x^2 + y^2 = z^2

anonymous · Answer

But I only have length of one side

perl · Answer

z is constant, so dz/dt = 0

perl · Answer

z is the length of the ladder, that doesnt change

perl · Answer

so 
2x(dx/dt)+2y(dy/dt)=2z(dz/dt) 
becomes
2x(dx/dt)+2y(dy/dt)=2z*0

2x(dx/dt)+2y(dy/dt)=0

anonymous · Answer

oh that makes a lot of sense thanks!

perl · Answer

and divide out 2