Calculus

posted by .

a ladder is 20 feet long and its top is slidding at a constant rate of 2 feet per second. How fast is the bottom of the ladder moving along the ground when the bottom is 16 feet from the wall?

  • Calculus -

    Let the ladder be x ft from the wall, and y ft up along the wall
    x^2 + y^2 = 20^2
    2x dx/dt + 2y dy/dt = 0
    x dx/dt + y dy/dt = 0
    when x=16 , y^2 = 400-256 ---> y = 12
    and dy/dt = -2 ft/sec

    16(dx/dt) + 12(-2) = 0
    dx/dt = -24/16 = -3/2

    the ladder is moving away from the wall at 1.5 ft/s

  • Calculus -

    last two lines should have been

    16(dx/dt) + 12(-2) = 0
    dx/dt = 24/16 = 3/2

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    A ladder 41 feet long that was leaning against a vertical wall begins to slip. Its top slides down the wall while its bottom moves along the level ground at a constant speed of 4 feet per second. How fast is the top of the ladder moving …
  2. calculus

    A 20 ft ladder is leaning against the side of a house. If the bottom of the ladder is moving away from the house at the rate of 2 feet per second, how fast is the top of the ladder moving down the wall when the bottom of the ladder …
  3. Calculus

    The top of a 24 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 4 feet per second. How fast is the bottom of the ladder sliding along the ground when the bottom of the ladder is 7 feet away from …
  4. Calculus

    A 17 foot ladder is leaning against a wall. The bottom of the ladder is moving out away from the wall at 0.6 feet per second. The top of the ladder then begins sliding down the wall. How fast is the top of the ladder going when the …
  5. Calculus

    A ladder 15 feet long leans against a vertical wall. Supppose that when the bottom of the ladder is x feet from the wall, the bottom is being pushed towards the wall at the rate of 1/2x feet per second. How fast is the top of the ladder …
  6. Calculus

    A ladder 25 feet long that was leaning against a vertical wall begins to slip. Its top slides down the wall while its bottom moves along the lever ground at a constant speed of 4 ft/sec. How fast is the top of the ladder moving when …
  7. calculus

    a ladder 6 feet long leans against a vertical building. the bottom of the ladder slides away from the building horizontally at rate of 1/2 ft/sec. A) at what rate is the top of the ladder sliding down the wall when the bottom of the …
  8. calculus

    A ladder 13 feet long is leaning against the side of a building. If the foot of the ladder is pulled away from the building at a constant rate of 8 inches per second, how fast is the area of the triangle formed by the ladder, the building, …
  9. Calculus

    a 12 foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 1 feet/second, how fast is the top of the ladder moving down when the foor of the ladder is …
  10. Calculus

    a 14 foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 3 feet/second, how fast is the top of the ladder moving down when the foor of the ladder is …

More Similar Questions