MATH

An airplane is flying in the direction 148° with an airspeed of u = 865 kilometers per hour. Because of the wind, its groundspeed and direction are v = 780 kilometers per hour and 140°, respectively (see figure in the link below). Find the direction and speed of the wind. (Round your answers to one decimal place.)
www.webassign.net/larpcalclim2/6-3-101-alt.gif

speed: (in km/h)
direction: N ? ° E

but the answer i got was:
speed: 142.68
direction: N 1.25 ° E
but i got the direction wrong and the speed correct?

  1. 👍 0
  2. 👎 0
  3. 👁 512
asked by ghost
  1. I did it using vectors, and then again using the cosine law, and got the same 142.68 as you did

    according to the wording as well as your diagram,
    let the wind vector be v
    v^2 = 865^ + 780^2 - 2(865)(780)cos8°
    v = 142.679 , you had that.
    then by the sine law in your diagram
    sinø/780 = sin8/142.679
    ø = 49.5° , with a bit of geometry using supplementary angles and parallel lines
    the direction of the wind is 49.5 - 40 or 9.5°

    Using vectors
    vector v = 865(cos148,sin148) - 780(cos140,sin140)
    = (-733.5616, 458.38) - (-597.515, 501.3743)
    = (-136.047, -42.994)
    |v| = √((-136.047)^2 + (-42.994)^2) = appr142.679 , same as before
    tan(direction angle) = -42.994/-136.047 = .316..
    direction angle = 17.54°

    (perhaps you can check my arithmetic to see why they are not the same,
    I can't locate my error at this point)

    1. 👍 0
    2. 👎 0
    posted by Reiny
  2. thanks Reiny, your answers is correct because i submitted 142.68 and 17.54 and it is correct

    1. 👍 0
    2. 👎 0
    posted by ghost

Respond to this Question

First Name

Your Response

Similar Questions

  1. trig

    An airplane is flying in the direction 148° with an airspeed of u = 920 kilometers per hour. Because of the wind, its groundspeed and direction are v = 820 kilometers per hour and 140°, respectively (see figure). Find the

    asked by bob on November 2, 2015
  2. PreCalc - Vectors

    An airplane is flying with an airspeed of 660 Kilometers per hour. The wind is blowing from 345 degrees at 35 km/h. What direction should the airplane take so that, with the wind, the plane will be flying in a direction of 72

    asked by Joe on May 3, 2011
  3. trigo

    An airplane travels on a bearing of 245 degrees at an airspeed of 200 kilometers per hour while a wind is blowing 50 kilometers per hour from 140 degrees. Find the ground speed of the airplane and the direction of its track, or

    asked by thomas on September 16, 2014
  4. Math

    An airplane has an airspeed of 724 kilometers per hour at a bearing of 30 degrees.The wind velocity is 32 kilometers per hour from the west. What are the groundspeed and the direction of the plane?

    asked by Matt on February 16, 2011
  5. Math- Please Help!!

    An airplane has an airspeed of 724 kilometers per hour at a bearing of 30 degrees.The wind velocity is 32 kilometers per hour from the west. What are the groundspeed and the direction of the plane?

    asked by Kourt on February 18, 2011
  1. Math

    An airplane has an airspeed of 724 kilometers per hour at a bearing of 30 degrees.The wind velocity is 32 kilometers per hour from the west. What are the groundspeed and the direction of the plane?

    asked by Kourt on February 18, 2011
  2. trig

    An airplane has an airspeed of 450 kilometers per hour bearing Upper N45E. The wind velocity is 60 kilometers per hour in the direction Upper N30W. Find the resultant vector representing the path of the plane relative to the

    asked by Ashley on May 2, 2017
  3. Physics

    An airplane has to fly eastward to a destination 865 km away. If wind is blowing at 18.8 m/s northward and the airspeed of the plane is 166 m/s, in what direction should the plane head to reach its destination?

    asked by Jillian on October 8, 2019
  4. Math

    An airplane is flying at an airspeed of 500 km/hr in a wind blowing at 50 km/hr toward the southeast. In what direction should the plane head to end up going due east? (Round your answer to two decimal places.)What is the

    asked by Kristen on August 28, 2015
  5. Trig

    The problem is: an airplane is flying in the direction 120 degrees with an airspeed of 320 mph, and a 35 mph wind is blowing in the direction 60 degrees. The question ask to find the true course and the ground speed. To solve the

    asked by Morgan on June 2, 2014

More Similar Questions