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Question 12 • Precalculus

Two planes take off from the same airport at approximately the same time. Plane A has an airspeed of 600 mph and travels in the direction cap s 20 degrees cap w Plane B has an airspeed of 450 mph and travels in the direction cap n 35 degrees cap e Which diagram represents the distance, x , between the planes?

Answer
A
Image with description On a coordinate plane, a vector labeled 450 miles per hour goes up and to the right in quadrant 2 and forms angle alpha = 35 degrees with the y-axis. A vector labeled 600 miles per hour goes down and to the right in quadrant 4 and forms angle beta = 20 degrees with the y-axis. Vector x goes from terminal point 600 miles per hour to terminal point 450 miles per hour.
B
Image with description On a coordinate plane, a vector labeled 450 miles per hour goes up and to the right in quadrant 1 and forms angle alpha = 35 degrees with the y-axis. A vector labeled 600 miles per hour goes down and to the right in quadrant 4 and forms angle beta = 20 degrees with the y-axis. Vector x goes from terminal point 600 miles per hour to terminal point 450 miles per hour.
C
Image with description On a coordinate plane, a vector labeled 450 miles per hour goes up and to the left in quadrant 2 and forms angle alpha = 35 degrees with the y-axis. A vector labeled 600 miles per hour goes down and to the left in quadrant 3 and forms angle beta = 20 degrees with the y-axis. Vector x goes from terminal point 600 miles per hour to terminal point 450 miles per hour.
D
Image with description On a coordinate plane, a vector labeled 450 miles per hour goes up and to the right in quadrant 1 and forms angle alpha = 35 degrees with the y-axis. A vector labeled 600 miles per hour goes down and to the left in quadrant 3 and forms angle beta = 20 degrees with the y-axis. Vector x goes from terminal point 600 miles per hour to terminal point 450 miles per hour.

Explanation

Plane A’s direction, S 20° W, points south and west, so its vector lies in quadrant III and is 20° from the y-axis. Plane B’s direction, N 35° E, points north and east, so its vector lies in quadrant I and is 35° from the y-axis. The distance vector x connects the planes’ endpoints, which matches diagram A.

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