If a wind begins blowing from the southwest at a speed of 100 km/h (average), ca

Question

If a wind begins blowing from the southwest at a speed of 100 km/h (average), calculate the velocity (magnitude) of the plane relative to the ground. [Hint: First draw a diagram.| Constants Express your answer to three significant figures and include the appropriate units. An airplane is heading due south at a speed of 620 km/h Value Units Submit X Incorrec; Try Again; 5 attempts remaining Part B Cakculate the velocity (direction) of the plane relative to the ground Express your answer to three significant figures and include the appropriate units Value Units east of south Submit PartC Calculate how far from its intended position will t be after 14 min if the pilot takes no corrective action Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

1)
the components of the airplane alone = (0, - 620)
components of wind alone = (100*cos45, 100*sin45)

components of plane + wind = (0 + 100cos45, - 620 + 100sin45)
= (70.71, - 690.71)

magnitude = (7071^2+690.71^2) = 694.319 km/h ( speed over ground)
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2) direction = tan^-1(690.71/70.71) = 84.15° south of east (below +x-axis)
____________
3) 14 min = 14/60 of an hour, so the intended position after 14 min =
(0, 620*14/60) = (0, 144.66)

the real position is (70.71*14/60, 690.71*14/60)
= (16.499, 161.165)

distance between intended, and real position
= ((16.499^2 + (161.165-144.66)^2)
= 23.33 km

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