Ask Question
18 April, 21:51

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)

+2
Answers (1)
  1. 18 April, 22:14
    0
    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
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “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 ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers