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Instruments in airplane A indicate that with respect to the air the plane is headed 30◦ north of east with an airspeed of 300 mi/h. At the same time radar on ship B indicates that the relative velocity of the plane with respect to the ship is 280 mi/h in the direction 33◦ north of east. Knowing that the ship is steaming due south at 12 mi/h, determine (a) the velocity of the airplane, (b) the wind speed and direction.

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Answer:

velocity of the plane = 274 miles/hour at 30.9⁰

velocity and direction of the wind = 26.7 miles/hour at 20.8⁰

Explanation:

Let the velocities be resolved using the vector method.

Let the x - axis be directed to the east

similarly, we shall direct the y axis upwards- to the north

Airspeed is given by

300 mil/h. (30⁰) = 300 (cos30⁰i + sin 30⁰j

plane relative to ship

= 12 miles/hour

= 12j

  • velocity of the plane is given by:

v =[tex]A_{p}[/tex]  + Vijb

  = -12 j + 280 (cos 33⁰i + sin 33⁰j)

  = 234.83 i + 140.50 j

[tex]V_{a}[/tex] = 274 miles per hour

  • velocity of the wind is given by the following equation:

[tex]v_{w} = +WIA= A-[/tex]

    = 234.831 + 140.50J - 300(cos 30⁰i + sin 30⁰j)

   = -24.98i - 9.50 j

   = 26.7 miles per hour at 20.8⁰

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