Question

A glider lands 26 miles west and 12 miles south from where it took off. The result of the trip can be described by the vector (-26, -12). What is another description of this vector using distance (for magnitude) and direction?

A) about 29 miles at 25 degrees south of west
B) about 25 miles at 29 degrees south of east
C) about 29 miles at 25 degrees
D) about 25 miles at 29 degrees south of west

Answer 1

The student's glider trip vector described by traveling 26 miles west and 12 miles south can be represented as being approximately 29 miles at an angle of 25 degrees south of west.

Step-by-step explanation:

To describe the glider's trip of 26 miles west and 12 miles south using distance (magnitude) and direction, we can calculate the resultant vector's magnitude using the Pythagorean theorem and the angle using basic trigonometry.

Magnitude: √((-26)^2 + (-12)^2) = √(676 + 144) = √820 ≈ 28.6 miles.

To find the direction, we calculate the angle θ in the south of west direction using the inverse tangent function (tan⁻¹), which gives:

θ = tan⁻¹(opposite/adjacent) = tan⁻¹(12/26) ≈ 25 degrees.

Therefore, the vector can be described as being around 29 miles at 25 degrees south of west.

The correct answer is: A) about 29 miles at 25 degrees south of west.