A plane is flying west at 500 ft/sec at an altitude of 4000 ft. The plane is tracked by a searchlight on the ground. If the light is to be trained on the plane, find the change in the angle of elevation of the searchlight at horizontal distance of 2000 ft.

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. tan(elevation)=4000/x
    d/dx tanE =-4000/x^2 dx/dt
    but d/dttanE= sec^2E * dE/dt

    sec^2 E * dE/dt=-4000/x^2 dx/dt

    solve for dE/dt when x=2000, You can figure secE from the triangle. You are given dx/dt as 500ft/sec

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    A plane is flying at an altitude of 12,000 feet and is preparing to land at a nearby airport. The angle from the airport to the plane is 17. To the nearest tenth of a foot, how far is the airport from the plane?

  2. Math

    Me, again... Please help me. Thank you. Assume a plane is flying directly north at 200 mph, but there is a wind blowing west at 23 mph. Part I: Express both the velocity of the plane and the velocity of the wind as vectors, using

  3. physics

    A plane is found by radar to be flying 5.9 km above the ground. The angle of elevation from the radar to the plane is 78.6°. Ten seconds later, the plane is directly over the station. Find the speed of the plane, assuming that it

  4. Mathematics

    A plane is flying at an altitude of 12000 m. From the pilot the angle of depression to the airport tower is 32°. How far is the tower from the point directly beneath the plane? Round to the nearest thousandth.

  1. Math

    A plane was flying at an altitude of 30,000 feet when it began the descent toward the airport. The airplane descends at a rate of 850 feet per minute. a. What is the function rule that describes this situation? b. What is the

  2. Physics

    Two planes are about to drop an empty fuel tank. At the moment of release each plane has the same speed of 135 m/s, and each tank is at the same height of around 2.00km above the ground. Although the speeds are the same, the

  3. MATH

    Two planes leave an airport at the same time, one flying east, the other flying west.The eastbound plane travels 100 mph slower. They are 3040mi apart after 4hrs. find the speed of each plane

  4. geometry

    An observer (O) spots a plane flying at a 55° angle to his horizontal line of sight. If the plane is flying at an altitude of 21,000 ft., what is the distance (x) from the plane (P) to the observer (O)?


    A plane is flying due South (270º) at 474.8 km/h. A wind blows from West to East (0°) at 46 km/h. Find the direction of the plane's travel. Report your answer in degrees from 0° as a reference.

  2. Geometry/trig

    A plane is flying due south at a speed of 300 mph. The wind is blowing from the west at a speed of 40 mph. Find the resultant speed of the plane and the direction of the plane

  3. Maths

    A plane is flying at an altitude of 880 m. Sarah is standing on the ground and she observes the angle of elevation to the plane as 67'40'. Twenty-five seconds later the angle of elevation had changed to 24'30'. (a) How far has the


    A plane, flying horizontally at an altitude of 1 km and a speed of 500 km/hr, passes directly over a radar station. find the rate in km/hr at which the distance from the plane to the station is changing when it is 2 km away from

View more similar questions or ask a new question.