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?

anonymous · Answer

x²  +  y²    =    z²
->      y     =    √ (15²  - 10²)   = 5√5 ft

xx'  + yy'   =    0
->        y'   =    - xx' / y
After 12 seconds:
                 =    - 3 ( -.25) / 5√5