Calculus some1 plz!!!!

posted by .

A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is π/3, this angle is decreasing at a rate of π/4 rad/min. How fast is the plane traveling at that time? (Round your answer to two decimal places.)

  • Calculus some1 plz!!!! -

    x = 12
    x' = -13/10
    y' = ? when x = 4
    m = 2
    y = ?

    Use proportiions.

    12 / 2 = 4 / y
    6 = 4 / y
    2/3 = y

    12 / x = 4 / y

    Differentiating both sides with respect to time, we get:

    -12 / x^2 * x' = -4 / y^2 * y'
    -12 / 4^2 * x' = -4 / (2/3)^2 * y'
    -12 / 16 * x' = -9 y'
    -3/4 * -13/10 = -9 y'
    39 / 40 = -9 y'
    -39 / 360 = y'
    -0.11 m/s = y'

    --------------------------------------…

    y = 5
    a = pi/4
    a' = -pi/3
    x' = ? when a = pi/4
    x = ?

    Let's first find x.

    tan(a) = opposite / adjacent
    tan(a) = y / x
    tan(pi/4) = 5 / x
    1 = 5/x
    5 = x

    Now we can rewrite as:

    tan(a) = 5 / x

    Now let's differentiatite both sides with respect to time. Doing so gives:

    a' * sec^2(a) = -5 / x^2 * x'
    -pi/3 * (1+tan^2a) = -5 / 25 * x'
    -pi/3 * (1 + tan^2(pi/4)) = -1/5 * x'
    -pi/3 * 2 = -1/5 * x'
    -2pi/3 * -5 = x'
    10pi/3 = x'
    10.47 km/min = x'


    Hope this helped.

  • Calculus some1 plz!!!! -

    sadly, it didn't work :( thanks for trying

  • Calculus some1 plz!!!! -

    x=h*cot(θ)
    dx/dθ=-h*csc²(θ)
    Given
    h=5 km
    dθ/dt = -π/4
    θ=π/3
    dx/dt=(dx/dθ)*d(θ/dt)
    =-h*csc²(θ)*dθ/dt
    =-5csc²(π/3)*(-π/4)
    =-5*(√3)/2*(-π/4)
    =1.083π/min.
    =3.40 km/min (not a fast plane!)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus test tomorrow

    A plane flying with a constant speed of 24 km/min passes over a ground radar station at an altitude of 5km and climbs at an angle of 35 degrees. At what rate, in km/min, is the distance from the plane to the radar station increasing …
  2. Calculus

    An airplane flies at an altitude of 5 miles toward a point directly over an observer. The speed of the plane is 600 miles per hour. Find the rate at which the angle of elevation tetra is changing when the angle is 30 degrees
  3. Math

    Hi, I am doing a practice exam, and I came across this problem and I am have difficultly starting it. A UFO flies horizontally at a constant speed at an altitude of 15 km and passes directly over a tracking telescope on the ground. …
  4. advance geometry

    A plane is flying east, ascending at a constant angle. Jack is standing on the ground, watching the plane come to (horizontally) directly at him. When he first sees the plane, at an angle of elevation of 15 degrees, its horizontal …
  5. A plane flies horizontally at an altitude of 5 km

    A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is π/3, this angle is decreasing at a rate of π/4 rad/min. How fast is the plane traveling …
  6. Calculus-rates

    1.) A man 6 ft tall walks at a rate of 5 ft per sec. from a light that is 15 ft above the ground. At what rate is the top of his shadow changing?
  7. Calculus

    A plane flying with a constant speed of 4 km/min passes over a ground radar station at an altitude of 5 km and climbs at an angle of 45 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing …
  8. Calculus Help

    A plane flies horizontally at an altitude of 6 km and passes directly over a tracking telescope on the ground. When the angle of elevation is π/3, this angle is decreasing at a rate of π/3 rad/min. How fast is the plane traveling …
  9. calc

    A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is π/3, this angle is decreasing at a rate of π/3 rad/min. How fast is the plane traveling …
  10. Trigonometry application

    I need help with this problem. am having trouble solving this. A rocket tracking station has two telescopes A and B placed 1.7 miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after …

More Similar Questions