A 15 foot ladder is resting against the wall. The bottom is initially 10 feet away from the wall and is being pushed towards the wall at a rate of 1/4 ft/sec. How fast is the top of the ladder moving up the wall 12 seconds after we start pushing?

Question

A 15 foot ladder is resting against the wall.  The bottom is initially 10 feet away from the wall and is being pushed towards the wall at a rate of  1/4 ft/sec.  How fast is the top of the ladder moving up the wall 12 seconds after we start pushing?

perl · Answer

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perl · Answer

x^2 + y^2 = z^2

2x * dx/dt  + 2y*dy/dt = 2z * dz/dt 

divide out 2 

z is constant, so dz/dt  = 0 

x*dx/dt + y * dy/dt = 0

perl · Answer

A 15 foot ladder is resting against the wall. The bottom is initially 10 feet away from the wall and is being pushed towards the wall at a rate of 1/4 ft/sec. How fast is the top of the ladder moving up the wall 12 seconds after we start pushing?

so x = 10, dx/dt = -1/4  , and solve for dy/dt

perl · Answer

10*(-1/4) + y * dy/dt = 0

we can find y by using pythagorean theorem

10^2 + y^2 = 15^2