math

A ladder , 5 meter long , standing on a horizontal floor , leans against a vertical wall . If the top of the ladder slides downwards at the rate of 10 cm/sec . Find the rate at which the angle between the floor and the ladder is decreasing when the lower end of the ladder is 2 meter from the wall .

  1. 👍 0
  2. 👎 0
  3. 👁 301
  1. let the ladder reach h m high on the wall, let the base angle be Ø
    sinØ = h/5
    h = 5sinØ
    dh/dt = 5cosØ dØ/dt

    given: dh/dt = -10m/sec
    when base = 2m, cosØ = 2/5

    -10 = 5(2/5) dØ/dt
    dØ/dt = -5 radians/sec

    the angle is decreasing at a rate of 5 radians / sec

    (by using the word "decreasing" I do not include the negative sign)

    1. 👍 0
    2. 👎 0
  2. Change first 5m to 500cm and 2m to 200cm and then solve using above procedure of reiny answer is 1/20 radians/sec

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Pre-Calculus

    A ladder leans leans against a building that has a wall slanting away from the ladder at an angle of 96 degrees with the ground. If the bottom of the ladder is 23 feet from the base of the wall and it reaches a point 52 feet up

    asked by K.C on March 4, 2011
  2. math

    A ladder 10 m long rests on horizontal ground and leans against a vertical wall. The foot of the ladder is pulled away from the wall at 2 m/s. How fast is the top sliding down the wall when the foot of the ladder is 6m from the

    asked by Grant on May 3, 2013
  3. physics help!

    A uniform stationary ladder of length= 5.1 m and mass= 15 kg leans against a smooth vertical wall, while its bottom legs rest on a rough horizontal floor. The coefficient of static friction between floor and ladder is μ = 0.41.

    asked by Michelle on April 10, 2014
  4. math

    A ladder is 13.0m long. It leans against the wall. The base of the ladder is 3.7m from the wall. What is the angle of inclination of the ladder to the nearest tenth of a degree?

    asked by liya on June 4, 2014
  1. math

    A ladder leans against a building. The angle of elevation of the ladder is 70°. The top of the ladder is 25 ft from the ground. To the nearest tenth of a foot, how long is the ladder?

    asked by TheOneNotHere on June 4, 2014
  2. Calculus (related rates)

    A ladder 13 meters long rests on horizontal ground and leans against a vertical wall. The foot of the ladder is pulled away from the wall at the rate of 0.4 m/sec. How fast is the top sliding down the wall when the foot of the

    asked by Craig on March 21, 2017
  3. Physics

    A 100N uniform ladder, 8.0m long, rests against a smooth vertical wall. the coefficient of static friction between ladder and the floor is 0.40. What minimum angle can the ladder make with the floor before it slips? im thinking

    asked by natali on November 11, 2007
  4. geometry

    the triangles formed by two ladders leaning against a wall are similar. how long is the shorter ladder? the first ladder is 42ft and leans against the wall at 24ft, and the shorter ladder leans against the wall at 8ft.

    asked by key on March 10, 2020
  1. calculus

    A ladder 29 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed

    asked by milly on February 19, 2016
  2. mathematic

    A ladder 10 meter long is leaning against a wall. If the top of the ladder is sliding down the wall at 3m/s, how fast is the angle between the top of the ladder and the wall changing when the foot of the ladder is 6 meter away

    asked by skullhong on March 22, 2012
  3. Physics

    A 6m long uniform ladder which has a mass of 25kg leans with its upper end against a smoorth vertical wall and its lower end on rough horizontal ground. The base of the ladder is 3m from the wall and a man of mass 70kg is two

    asked by Tyrone on October 8, 2014
  4. Trig

    A 12 foot ladder leans against a building. The top of the ladder leans against the wall 10.5 feet from the ground. What is the angle formed by the ground and the ladder? Assume its a right triangle.

    asked by Charlie on April 17, 2013

You can view more similar questions or ask a new question.