A plane is traveling with an airspeed of 350 mph in the direction cap n 40 degrees cap e Let the plane’s ground speed equal x , which is affected by a 50 -mph wind blowing directly from the south. Which diagram represents this scenario?
Answer
A
Image with description On a coordinate plane, a vector labeled 350 miles per hour is 40 degrees from the y-axis in quadrant 1. Vector x is about 35 degrees from the y-axis. A vector labeled 50 miles per hour connects the terminal points of the 2 vectors.
B
Image with description On a coordinate plane, a vector labeled 350 miles per hour is 40 degrees from the y-axis in quadrant 2. Vector x is about 35 degrees from the y-axis. A vector labeled 50 miles per hour connects the terminal points of the 2 vectors.
C
Image with description On a coordinate plane, a vector labeled 350 miles per hour is 40 degrees from the x-axis in quadrant 2. Vector x is about 45 degrees from the x-axis. A vector labeled 50 miles per hour connects the terminal points of the 2 vectors.
D
Image with description On a coordinate plane, a vector labeled 350 miles per hour is 40 degrees from the x-axis in quadrant 1. Vector x is about 45 degrees from the x-axis. A vector labeled 50 miles per hour connects the terminal points of the 2 vectors.
Explanation
“N 40° E” means the plane’s 350-mph airspeed points 40° east of north, so it lies in quadrant I and is measured from the y-axis. The wind blows from the south toward the north, so adding it increases the northward component of the plane’s velocity; the resulting ground-speed vector x is therefore a little closer to the y-axis, at about 35° from it. This matches the diagram showing the 50-mph wind between the airspeed and ground-speed vectors.
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