Question

a pilot flies in a straight path for 1 h 30 min. she then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 h in the new direction. if she maintains a constant speed of 640 mi/h, how far is she from her starting position?

Answer 1

The pilot flies 960 miles in the first leg and 1280 miles in the second leg. By applying the law of cosines with these distances and the 10-degree angle, we can calculate the total distance from the starting point.

Step-by-step explanation:

To determine how far the pilot is from her starting position, we need to use the concept of vector addition. The first leg of her journey is in a straight path for 1 hour and 30 minutes (1.5 hours), and the second leg of the journey is after a course correction, heading 10 degrees to the right, for 2 hours. Flying at a constant speed of 640 mi/h, we can calculate the distance for each leg and then apply the law of cosines to find the total distance from the starting point.

First leg distance:
Distance = speed × time = 640 mi/h × 1.5 h = 960 miles

Second leg distance:
Distance = speed × time = 640 mi/h × 2 h = 1280 miles

To find the total distance from the starting point (R), we use the law of cosines:

R2 = 9602 + 12802 - 2(960)(1280)cos(10°)

After calculating R, we have the total distance from the starting point. This exercise resembles the physics problems involving vector addition and wind influence on an airplane's path.