A plane is flying in a storm. A GPS system measures the plane heading at an angl

Question

A plane is flying in a storm. A GPS system measures the plane heading at an angle 23 west of south, with a speed of 180 mph, relative to the ground. A nearby weather station measures the wind’s velocity to be 30 north of east, at a speed of 50 mph. Below, write a vector equation which gives the plane’s velocity relative to the air (v~P/A) in terms of its velocity relative to the ground (v~P/G) and the air’s velocity relative to the ground (v~A/G). Draw the corresponding vector addition (or subtraction) to the right. What is the magnitude and direction of the plane’s velocity, relative to the air? vP/A =

Velocity Magnitude=

Velocity Direction =

Explanation / Answer

plane velocity relative to ground

Vp/G = -180*sin23 i - 180*cos23 j

wind velocity relative to ground

VA/G = 50*cos30 i + 50*sin30 j

plane velocity relative to wind

Vp/A = vP/G + VG/A

VP/A = vP/G - vA/G

vP/A = (-180*sin23 - 50*cos30) i + (-180*cos23 - 50*sin30) j

VP/A = -114 i - 191 j

magnitude = 222.43 mph

direction = 31 degrees west of south

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