math

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 up 6 feet of the ladder, the ladder makes an angle of π/3 with the ground. Answer the two related rates questions below. (Hint: Use two carefully labeled similar right triangles.)

  1. 👍 0
  2. 👎 0
  3. 👁 648
  1. Almost forgot

    (b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is π/3, find dw/dt=

    1. 👍 0
    2. 👎 0
  2. Karthik,where is 2 questions??

    We draw a diagram with X=distance from wall to base of ladder.
    Z=distance along ladder that firefighter has climbed.
    H =height of firefighter
    W=distance from wall to firefighter
    Theta=angle of base of ladder with the ground.

    Ladder is sliding away at a constant rate of 3ft/sec------>dx/dt=3
    Firefighter is climbing up ladder at rate of 2ft/sec------->dz/dt=2
    Cos(theta)=x/29
    -sin(theta)d*theta/dt=1/29 dx/dt
    Please solve it.....
    B)
    Cos(theta)=w/(29/-z)
    W=(29-z)cos(theta)
    dw/dt=(-1 dz/dt)cos(theta)+(29-z)(-sin(theta) d(theta)/dt)
    dw/dt=-cos(theta)dz/dt-(29-z)sin(theta)d(theta)/dt

    Now you can solve the remaining portion...

    Hmm..I don't know whether it is right or not.OK

    1. 👍 0
    2. 👎 0
  3. I think that the θ is just a way of giving us the slope of the ladder. If the firefighter has climbed a distance z to a height h, then we have

    x^2+y^2 = 29^2
    w^2+(y-h)^2 = (29-z)^2

    when θ=π/3, x = 29/2 and y=29√3/2
    w = (29-z)/2 and h = z√3/2
    when z=6, then,
    w = 23/2 and h=3√3

    2x dx/dt + 2y dy/dt = 0
    2(29/2)(3) + 2(29√3/2) dy/dt = 0
    dy/dt = -√3

    See if you can finish it off, using the other equation.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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.

  2. algebra

    A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 feet and the length of the ladder is one foot more than twice the distance from the wall. Find the distance from the wall to the bottom

  3. Physics

    A ladder 20m long rest against a vertical wall so that the foot of the ladder is 9m long. Find correct to the nearest degree the angle that the ladder makes with the wall.

  4. Maths

    A ladder leans against a vertical wall of height 12m.if the foot of the ladder is 5m away from the wall,calculate the length of the ladder.

  1. Math

    A 25ft ladder leans up against the side of a house, with the base of the ladder a distance 3ft from the wall. If the ladder is moved out by 5ft, how far down the wall will the top of the ladder move?

  2. college algebra

    A contractor leans a 23-foot ladder against a building. The distance from the ground to the top of the ladder is 7 feet more than the distance from the building to the base of the ladder. How far up the building is the ladder to

  3. 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

  4. geometry/trig

    Initially a fifty foot ladder rests against a wall. As I start to climb it, the ladder slides down, finally stopping such that the ladder touches the wall at a point 8 feet below where it originally touched the wall. During the

  1. 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

  2. Calculus

    A contractor leans a 23-foot ladder against a building. The distance from the ground to the top of the ladder is 9 feet more than the distance from the building to the base of the ladder. How far up the building is the ladder to

  3. Trig

    The foot of a ladder is on level ground 1.5m from a wall. The ladder leans agents the wall. The angle formed by the ladder and the ground is 70 degrees. Calculate how high up the wall the ladder reaches.

  4. Calculus--Please Help!

    A 13-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away at a rate of 2 feet per second, how fast is the area of the triangle formed by the wall, the ground, and the ladder changing

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