An airplane leaves an airport at 9:00 p. M. With a heading of 270 and a speed of 610 mph. At 10:00 p. M. The pilot changes the heading to 310. Determine how far the plane is from the airport at 1:00 a. M.

2330.51 miles

Step-by-step explanation:

Given that the speed of the airplane = 610 mph.

The airplane leaves an airport at 9:00 P.M. with a heading of 270 degrees and at 10:00 P.M., the pilot changes the heading to 310 degrees.

So, for 1 hour the plane is heading at 270 degrees and for 3 hours, from 10:00 p.m to 1:00 a.m, the plane is heading at 310 degrees as shown in the figure.

As, distance = time x speed, so

The distance covered at 270 degrees, miles.

The distance covered at 310 degrees, miles.

Total distance covered, d, is the magnitude of the sum of vectors and as shown in the figure.

The angle between the vectors and , degree.

Magnitude of sum of the vectors \vec{d_1} and \vec{d_2},

miles

Hence, at 1:00 a.m, the airplane is at a distance of 2330.51 miles from the airport.

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