Question

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?

Answer 1

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

Answer 2

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

Answer 3

correct so far

Answer 4

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

Answer 5

But I only have length of one side

Answer 6

z is constant, so dz/dt = 0

Answer 7

z is the length of the ladder, that doesnt change

Answer 8

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

Answer 9

oh that makes a lot of sense thanks!

Answer 10

and divide out 2