AnswersPrecalculusApplying Vectors in the Plane

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An airplane is heading due north at 700 kph, and a wind blows at 60 kph in the direction S 45° E. What is the plane’s ground speed?

A
640.00 kph
B
658.94 kph
C
700.00 kph
D
743.64 kph
2
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Which diagram indicates a bearing of S 40° E?

A
On a coordinate plane, vector u goes down and to the right in quadrant 4 and forms angle 40 degrees with the y-axis.
Option A
B
On a coordinate plane, vector u goes down and to the right in quadrant 3 and forms angle 40 degrees with the y-axis.
Option B
C
On a coordinate plane, vector u goes down and to the right in quadrant 2 and forms angle 40 degrees with the y-axis.
Option C
D
On a coordinate plane, vector u goes down and to the right in quadrant 1 and forms angle 40 degrees with the y-axis.
Option D
3

Review the diagram.

Question illustration
A
409.81 pounds
B
600.00 pounds
C
653.91 pounds
D
859.81 pounds
4

Review the graph.

Question illustration
A
13.23 pounds
B
38.78 pounds
C
43.95 pounds
D
53.23 pounds
5

Review the diagram.

Question illustration
A
approximately 85 m
B
approximately 122 m
C
approximately 174 m
D
approximately 194 m
6

An airplane is traveling with an airspeed of 500 mph in the direction N 60° E. A wind blows directly south at 50 mph. What is the plane’s drift angle?

A
3.84°
B
5.21°
C
60.00°
D
65.21°
7

Review the diagram.

Question illustration
A
(78, 290)
B
(290, 78)
C
(127, 272)
D
(272, 127)
8

Review the diagram.

Question illustration
A
approximately 85 m
B
approximately 122 m
C
approximately 174 m
D
approximately 194 m
9

Review the diagram.

Question illustration
A
approximately 37.00° above the ground
B
approximately 42.17° above the ground
C
approximately 47.83° above the ground
D
approximately 53.00° above the ground
10

Review the diagram.

Question illustration
A
(78, 290)
B
(290, 78)
C
(127, 272)
D
(272, 127)
11

A boat travels with velocity vector . What is the directional bearing of the boat?

Question illustration
A
N 30° E
B
E 30° S
C
E 30° N
D
N 30° W
12

Review the diagram.

Question illustration
A
9,821 pounds
B
10,244 pounds
C
14,405 pounds
D
24,226 pounds
13

A plane is traveling with an airspeed of 350 mph in the direction N 40° E. Let the plane’s ground speed equal x, which is affected by a 50-mph wind blowing directly from the south. Which diagram represents this scenario?

A
On a coordinate plane, a vector labeled 350 miles per hour is 40 degrees from the y-axis in quadrant 1. Vector x is about 35 degrees from the y-axis. A vector labeled 50 miles per hour connects the terminal points of the 2 vectors.
Option A
B
On a coordinate plane, a vector labeled 350 miles per hour is 40 degrees from the y-axis in quadrant 2. Vector x is about 35 degrees from the y-axis. A vector labeled 50 miles per hour connects the terminal points of the 2 vectors.
Option B
C
On a coordinate plane, a vector labeled 350 miles per hour is 40 degrees from the x-axis in quadrant 2. Vector x is about 45 degrees from the x-axis. A vector labeled 50 miles per hour connects the terminal points of the 2 vectors.
Option C
D
On a coordinate plane, a vector labeled 350 miles per hour is 40 degrees from the x-axis in quadrant 1. Vector x is about 45 degrees from the x-axis. A vector labeled 50 miles per hour connects the terminal points of the 2 vectors.
Option D
14

Review the diagram.

Question illustration
A
409.81 pounds
B
600.00 pounds
C
653.91 pounds
D
859.81 pounds
15

A plane flies at 350 mph in the direction 40° north of east, with a wind blowing at 40 mph in the direction 30° south of east. What is the plane’s drift angle?

A
5.90°
B
6.38°
C
45.89°
D
46.38°
16

An airplane travels at 300 mph in the direction S 45° E. What is the component form of the velocity vector?

A
(150 StartRoot 2 EndRoot, 150 StartRoot 2 EndRoot)
Option A
B
(150 StartRoot 2 EndRoot, negative 150 StartRoot 2 EndRoot)
Option B
C
(negative 150 StartRoot 2 EndRoot, 150 StartRoot 2 EndRoot)
Option C
D
(negative 150 StartRoot 2 EndRoot, negative 150 StartRoot 2 EndRoot)
Option D
17

An airplane is headed due south with an airspeed of 300 kph. A wind is blowing from the west at 120 kph. What is the ground speed and direction of the plane?

A
323 kph with a directional bearing of S 22° E
B
328 kph with a directional bearing of S 68° E
C
420 kph with a directional bearing of S 22° E
D
420 kph with a directional bearing of S 68° E
18

A single-engine plane is flying at 30 mph in the direction N 60° E. A wind is blowing from west to east at 15 mph. Which diagram accurately represents the wind triangle for this plane?

A
On a coordinate plane, a ground vector goes up and to the right. Air vector is higher than the ground vector and forms angle 60 degrees with the x-axis. Wind vector connects the terminal points of the vectors.
Option A
B
On a coordinate plane, an air vector goes up and to the right. Ground vector is higher than the ground vector and forms angle 60 degrees with the x-axis. Wind vector connects the terminal points of the vectors.
Option B
C
On a coordinate plane, a ground vector goes up and to the right. Air vector is higher than the ground vector and forms angle 60 degrees with the y-axis. Wind vector connects the terminal points of the vectors.
Option C
D
On a coordinate plane, an air vector goes up and to the right. Ground vector is higher than the ground vector and forms angle 60 degrees with the y-axis. Wind vector connects the terminal points of the vectors.
Option D

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