The figure shows a small plane flying at a speed of 180 miles per hour on a bearing of N50°E. The wind is blowing from west to east at 40 miles per hour. The figure indicates that v represents the velocity of the plane in still air and w represents the velocity of the wind. Find,
a). Express v and w in terms of their magnitudes and direction angles.
b). Find the resultant vector, v + w.
c). The magnitude of v + w, called the ground speed of the plane, gives its speed relative to the ground. Approximate the ground speed to the nearest mile per hour.
d). The direction angle of v + w gives the plane’s true course relative to the ground. Approximate the true course to the nearest tenth of a degree. What is the plane’s true bearing?
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