Ask Question
12 March, 15:03

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)

+5
Answers (1)
  1. 12 March, 16:01
    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 you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers