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

  1. 👍 0
  2. 👎 0
  3. 👁 1,537
  1. Let
    angle of elevation=θ
    height of plane = H
    horizontal distance from observer = x

    Use implicit differentiation
    d(tan(θ))/dt = d(x/H)/dt
    sec²(θ)dθ/dt = (dx/dt)/H
    Can you take it from here?

    1. 👍 0
    2. 👎 0
  2. would you just replace H with 5 miles since that's the height the plane is flying at?

    1. 👍 0
    2. 👎 0
  3. This is where you need to do some work.
    The formula is general, but the numerical values you substitute have to be consistent in units.

    For H=5 miles, and dx/dt=600 miles/hour, it would give dθ/dt in radians/hour.
    You need to substitute values in appropriate units of your choice. Finally, you can also change radians to degrees using degrees=radians*180/π.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    An airplane flys at a constant altitude of 2 miles and a constant speed of 600 miles per hour on a straight course that will take it directly over a kangaroo on the ground. How fast is the angle of elevation of the kangaroo's line

  2. math

    An airplane leaves Atlanta at 2 PM and flies north at 250 miles per hour. A second airplane leaves Atlanta 30 minutes later and flies north at 280 miles per hour. At what time will the second airplane overtake the first? Answer

  3. math

    A model airplane flies 18 feet in 2 seconds. what is the airplane's speed in miles per hour? round your answer to nearest hundredth.

  4. Physics

    An airplane flies 220 km due east, makes a right-angle, and then flies 400 km due north. Find the magnitude of the plane's displacement from it's starting point. Neglect the culrvature of the earth

  1. 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? 2.) An airplane flies at an altitude of 5 miles toward a point directly over an

  2. Physics

    "An airplane is climbing at an angle of 15 degrees to the horizontal with the sun directly overhead. The shadow of the airplane is observed to be moving across the ground at 200 km/h. How long does it take for the plane to

  3. Algebra 2. Please Help Someone!!

    an airplane's altitude is 100 feet as it descents for a landing on a runway whose touchdown is 5000 ft away. Let the x-axis represent the ground and the y-axis represent the airplane's altitude. What is the slope of the airplane's

  4. algebra 1

    a model airplane flies 18 feet in 2 seconds. What is the airplane's speed in miles per hour?

  1. algebra

    An airplane flies 750 miles due west in 1 1/2 hours and 750 miles due south in 2 hours. What is the average speed of the airplane?

  2. Trigonometry

    An airplane is sighted at the same time by two ground observers who are 2 miles apart and both directly west of the airplane. They report the angles of elevation as 11˚ and 20˚. How high is the airplane? Round to the nearest

  3. modern physics

    a hunter on the ground fires a bullet in the northeast direction which strikes a deer 0.25 metre away from him, the bullet travel with a speed of 1800m/ the instant an airplane is directly over the hunter at an altitude of


    Hot dogs and Hamburgers: 1.) The caterer for your class picnic charges $1 for each hotdog and $2 for each hamburger. You have $48 to spend. Write a model that shows the different numbers of hot dogs and hamburgers that you could

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