5. According to ground-based radar, an airplane is flying 15 degrees north of west at a...

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Answer 1

Answer #1

Given
the plane is flying with 100 mph at an angle of 15 degrees north of west relative to ground and

wind is blowing with velocity 35 mph, at an angle 45 degrees south of east ,

that is VPG = 100 mph, at an angle of 165 degrees from the +x-axis and

VWG = 35 mph , at an angle of 315 degrees from the + x-axis

VPW = ? ( speed of the plane relative to the air)

from the relation V_PG = V_PW +V_WG

V_PW = V_PG- V_WG
V_PG = 100 cos165 i +100 sin 165 j = -96.6 mph i+25.88 mph j

V_WG = 35 cos315 i + 35 sin 315 j = 24.75 mph i - 24.75 mph j

V_PW = (-96.6 + 24.75)mph i + (25.88-24.75) mph j

V_PW = (-71.85) mph i + 1.13 mph j

magnitude is

V_PW = sqrt( (-71.85)^2 +1.13^2) mph = 71.86 mph
so the speed of the plance relative to the air is 71.86 mph

Answer 2

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