When an airplane flies, its total velocity with respect to the ground is
vtotal = vplane + vwind,
where vplane denotes the plane's velocity through motionless air, and vwind denotes the wind's velocity. Crucially, all the quantities in this equation are vectors. The magnitude of a velocity vector is often called the “speed.”
Consider an airplane whose speed through motionless air is 100 meters per second (m/s). To reach its destination, the plane must fly east.
The “heading” of a plane is the direction in which the nose of the plane points. So, it is the direction in which the engines propel the plane.

1. | If the plane has an eastward heading, and a 20 m/s wind blows towards the southwest, then the plane's speed is:

A. | 80 m/s

B. | more than 80 m/s but less than 100 m/s

C. | 100 m/s

D. | more than 100 m/s

2. | The pilot maintains an eastward heading while a 20 m/s wind blows northward. The plane's velocity is deflected from due east by what angle?

A. | sin-1

B. | cos-1

C. | tan-1

D. | none of the above

3. | Let ø denote the answer to question 2. The plane in question 2 has what speed with respect to the ground?

A. | (100 m/s)sin ø

B. | (100 m/s)cos ø

C. |

D. |

4. | Because the 20 m/s northward wind persists, the pilot adjusts the heading so that the plane's total velocity is eastward. By what angle does the new heading differ from due east?

A. | sin-1

B. | cos-1

C. | tan-1

D. | none of the above

5. | Let q denote the answer to question 4. What is the total speed, with respect to the ground, of the plane in question 4?

A. | (100 m/s)sin q

B. | (100 m/s)cos q

C. |

D. |

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