Ask Question
19 May, 00:29

A 25-foot ladder is leaning against a house. The base of the ladder is pulled away from the house at a rate of 2 feet per second. How fast is the top of the ladder moving down the wall when the base is given below?

+4
Answers (1)
  1. 19 May, 00:34
    0
    A ladder 25 feet long is leaning against a house. The base of the ladder is pulled away at a rate of 2 ft/sec.

    a.) How fast is the top of the ladder moving down the wall when the base of the ladder is 12 feet from the wall?

    Answer:

    dy/dt = - 1.094ft/sec

    Explanation:

    Given that:

    dz/dt = 0,

    dx/dt = 2,

    dy/dt = ?

    Hence, we have the following

    Using Pythagoras theorem

    We have 25ft as the hypotenuse, y as the opposite or height of wall, and x as the base of the triangle

    X² + y² = z²,

    12² + y² = 25²,

    y² = 25² - 12²

    y = √481

    Therefore, we have the following:

    2x dx/dt + 2y dy/dt,

    = 2z dz/dt,

    = 12 (2) √481 dy/dt,

    = √481 dy/dt = - 24,

    = dy/dt = - 1.094ft/sec

    Therefore, final answer is - 1.094ft/sec
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “A 25-foot ladder is leaning against a house. The base of the ladder is pulled away from the house at a rate of 2 feet per second. How fast ...” in 📗 Physics 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