In this problem we use the subscript W to represent the air, which has a wind. Hence, we use the letter W to reference the air. The letter A stands for airplane. E stands for Earth. A pilot takes off from a city in Northern California and aims her airplane due North toward Seattle with a speed VAW (in km/h) relative to the air (wind), where Vw = 265.0 km/h. The air (wind) has an Eastward wind of speed VWE = 108.2 km/h relative to the Earth. The airplane lands at a small airport that is directly East of Seattle. The North-South distance between the takeoff location and Seattle is 1026.1 km. (a) What is the magnitude VAE of the airplane's velocity relative to the Earth? SEE THE GRAPH to get the magnitude of the resultant of the two vectors shown. (b) What is the direction of the airplane's velocity relative to the Earth? Find this direction by computing the angle this velocity makes with the North direction shown in the schematic of the problem below. HINT: SEE THE GRAPH and get the direction of the resultant of the two vectors shown. Get that angle that the resultant makes with the northward direction using trigonometry and the vector (c) How long (in hours h) does the airplane trip take? What is the Fastward distance between Seattle and the

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Chapter1: Units, Trigonometry. And Vectors
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1.
In this problem we use the subscript W to represent the
air, which has a wind. Hence, we use the letter W to reference the air.
The letter A stands for airplane. E stands for Earth.
A pilot takes off from a city in Northern California and aims her
airplane due North toward Seattle with a speed VAW (in km/h) relative to
the air (wind), where Vw = 265.0 km/h. The air (wind) has an
AW
Eastward wind of speed VWE = 108.2 km/h relative to the Earth. The
airplane lands at a small airport that is directly East of Seattle. The
North-South distance between the takeoff location and Seattle is 1026.1
km.
(a)
What is the magnitude VAE of the airplane's velocity
relative to the Earth? SEE THE GRAPH to get the magnitude of the
resultant of the two vectors shown.
(b)
What is the direction of the airplane's velocity relative to
the Earth? Find this direction by computing the ang this velocity
makes with the North direction shown in the schematic of the problem
below. HINT: SEE THE GRAPH and get the direction of the resultant
of the two vectors shown. Get that angle that the resultant makes with
the northward direction using trigonometry and the vector
(c)
(d)
How long (in hours h) does the airplane trip take?
What is the Eastward distance between Seattle and the
small airport that is directly East of Seattle?
265.0 km/h
108.2 km/h
N
-E
Transcribed Image Text:1. In this problem we use the subscript W to represent the air, which has a wind. Hence, we use the letter W to reference the air. The letter A stands for airplane. E stands for Earth. A pilot takes off from a city in Northern California and aims her airplane due North toward Seattle with a speed VAW (in km/h) relative to the air (wind), where Vw = 265.0 km/h. The air (wind) has an AW Eastward wind of speed VWE = 108.2 km/h relative to the Earth. The airplane lands at a small airport that is directly East of Seattle. The North-South distance between the takeoff location and Seattle is 1026.1 km. (a) What is the magnitude VAE of the airplane's velocity relative to the Earth? SEE THE GRAPH to get the magnitude of the resultant of the two vectors shown. (b) What is the direction of the airplane's velocity relative to the Earth? Find this direction by computing the ang this velocity makes with the North direction shown in the schematic of the problem below. HINT: SEE THE GRAPH and get the direction of the resultant of the two vectors shown. Get that angle that the resultant makes with the northward direction using trigonometry and the vector (c) (d) How long (in hours h) does the airplane trip take? What is the Eastward distance between Seattle and the small airport that is directly East of Seattle? 265.0 km/h 108.2 km/h N -E
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