A small plane flying at a speed of 180 miles per hour on a bearing of N50E. the wind is blowing from west to east at 40 miles per hour. Let v represent the velocity of the plane in still air and w represent the velocity of the wind.
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 and 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 planes true course relative to the ground. Approximate the true course to the nearest tenth of a degree. What is the planes true bearing?