is a pilot. Suppose his airplane flies in still air at a speed of 420 km/h. One

Question

is a pilot. Suppose his airplane flies in still air at a speed of 420 km/h. One day The wind is blowing strongly at 110 km/h towards the north. Prof. Jacome flies the plane from Manhattan to Miami, a due cast displacement on the ground. See the diagram, and identity the vectors for: the velocity of the plane relative to the ground? A B C the velocity of the plane relative to the air? A B C Calculate the direction that the airplane should head or point, so that its net motion is towards Miami. Express the result using points of the compass and an angle, 25 degrees west of north.

Explanation / Answer

Given

speed of airplane in still wind is Vpg = 420 kmph = 420*5/18 m/s = 116.67 m/s = C

and the wind speed is Vwg = 110 kmph = 110*5/18 m/s = 30.56 m/s = B

a) velocity of plane relative to ground is Vpg = C

b) velcocity of plane relative to air/wind is Vpw = B

using relative velocity

   V_pg = v_pw+v_wg

   V_pw = V_pg - v_wg
   = 116.67 - 30.56 m/s

   = 86.11 m/s
c)

now the direction of airplane to reach miame is tan theta = B/C

   theta = arc tan (B/C)
   = arc tan (30.56/116.67) degrees

   = 14.67 degrees south of east

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