A 25 ft ladder is leaning against a vertical wall. The bottom of the ladder is pulled horizontally away from the wall at 3 ft/sec. Determine how fast the top of the ladder is sliding when the bottom of the ladder is 15 ft from the wall. Please explain the process!

Question

A  25 ft ladder is leaning against a vertical wall.  The bottom of the ladder is pulled horizontally away from the wall at 3 ft/sec. Determine how fast the top of the ladder is sliding when the bottom of the ladder is 15 ft from the wall. Please explain the process!

anonymous · Answer

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differentiate the function x^2+y^2=25^2 with respect to time
2x dx/dt=-2y dy/dt
when x=15 y=20
given dx/dt = 3
find dy/dt which is the speed at which top falls , the negative sign just shows the direction of motion