A 15 foot ladder is leaning against one wall of an alley 9 ft wide. The ladder slips, its top sliding down the wall, it’s foot sliding across the alley and striking the opposite wall at a speed of 4 ft/sec. how fast is the top of the ladder falling at that instance? (Related rates problem)
This is question of differential equation The ladder will form a right triangle with the wall and floor let base of the triangle be x and perpendicular be y so x² + y² = 15², by Pythagoras now y=12 when x=9 (given) , differentiating x² + y² = 15² 2x dx/dt +2y dy/dt = 0 x dx/dt + y dy/dt = 0 given dx/dt= 4 ft/sec 9*4 + 12 dy/dt = 0 dy/dt = - 3 ft/sec
