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.

Answer 1

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