Trig

In still air, an airplane is flying at 100 mph. It encounters a wind blowing toward the west at 50 mph. What should be the plane's compass heading for its course to be N30ºW?

  1. 👍
  2. 👎
  3. 👁
  1. If the plane is flying on heading NθE, then we want

    100sinθ-50 = -v/2
    100cosθ = v √3/2

    100sinθ = 50-v/2
    100cosθ = v√3/2

    (50-v/2)^2 + 3/4 v^2 = 100^2
    v = 115.14

    So, cosθ = .997
    θ = 4.3º

    and the heading is N4.3ºE

    1. 👍
    2. 👎
  2. Could you explain the (50-v/2)^2 + 3/4v^2 = 100^2 part? I'm a little confused.

    1. 👍
    2. 👎
  3. square the previous equations and add them up. Recall that

    sin^2θ + cos^2θ = 1

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    An airplane cruises at 880km/h relative to the air. It is flying from Denver, Colorado due west to Reno, Neveda, a distance of 1200km and will then return. There is a steady 90km/h wind blowing to the east. What is the difference

  2. Trig/Precal

    An airplane flies on a compass heading of 90° at 310 mph. The wind affecting the plane is blowing from 332° at 40 mph. What is the true course and ground speed of the airplane?

  3. Trig

    An airplane is flying on a compass heading (bearing) of 340 degrees at 325 mph. A wind is blowing with the bearing 320 degrees at 40 mph. Find the component form of the velocity of the airplane. then find the actual ground speed

  4. Precalculus

    An airplane is flying on a bearing of 285 degrees at 480 mph. A wind is blowing with the bearing 265 degrees at 30? a. find the component from of the velocity of the airplane b. find the actual speed and direction of the airplane

  1. Trigonometry

    An airplane is traveling at 650 mph on a heading of 255°. The wind is blowing from a bearing of 320° at 28 mph. What is the ground speed and the actual bearing of the airplane? P.S. I prefer the law of cosine/sine method

  2. calculus

    An airplane is flying at 550 km/h on a heading of 080 degrees. The wind is blowing at 60 km/h from a bearing of 120 degrees. Find the ground velocity of the airplane and include the new bearing.

  3. algebra

    A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the

  4. trig

    An aifplane is flying on a compass heading (bearing) of 170* at 460 mph. A wind is blowing with the bearing 200* at 80mph. a) Find the component form of the velocity of the airplane. b) Find the actual ground speed and direction

  1. physics

    After flying for 15 min in a wind blowing 42 km/h at an angle of 20° south of east, an airplane pilot is over a town that is 42 km due north of the starting point. What is the speed of the airplane relative to the air?

  2. math

    An airplane is flying from Montreal to Vancouver. The wind is blowing from the west at 60km/hour. The airplane flies at an airspeed of 750km/h and must stay on a heading of 65 degrees west of north. A) what heading should the

  3. Physics

    The wind is blowing from west to east at 35 mph and an eagle in that wind in flying at 22 mph relative to the air what is the velocity of this eagle realtive to a person standing on the ground if the eagle is flying (a) from west

  4. calculus

    An airplane is flying on a bearing of 80 degrees at 540mph. A wind is blowing with a bearing of 100 degrees at 55mph. Find the component form of the velocity of the airplane.

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