Answer:

Part B: v+w=161.42i+136.36j
Part C: 211.3 mph
Explanation:
Part A
• The velocity of the plane in still air, v = 178 miles per hour.
,
• The angle v makes with the x-axis = 90°-40° = 50°
Therefore, vector v in terms of its magnitude and direction cosine is:

Similarly:
• The velocity of the wind, w = 47 miles per hour.
,
• The angle w makes with the x-axis = 0°
Therefore, vector w in terms of its magnitude and direction cosine is:

The correct option is A.
Part B
From part A:

Therefore, the resultant vector, v+w is:

Part C
The magnitude of v+w, called the ground speed, gives its speed relative to the ground.

The ground speed is 211.3 mph (rounded to the nearest tenth).