Multiple Choice
A small helicopter travels 225 m across a city in a direction 53.1° south of east. What are the components of the helicopter's trip?
3. Vectors
Trig Review
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The vector A represented is by the pair of components Ax = -77 cm, Ay = 36 cm. (a) Find the magnitude of vector A. (b) Find the absolute angle of this vector.
A
(a) A = 68 cm (b) 179.6°
B
(a) A = 85 cm (b) 179.6°
C
(a) A = 68 cm (b) 154.9°
D
(a) A = 85 cm (b) 154.9°
E
(a) A = 68 cm (b) −25.1°
F
(a) A = 85 cm (b) −25.1°
Verified step by step guidance1
To find the magnitude of vector A, use the Pythagorean theorem. The magnitude |A| is given by the formula: |A| = sqrt(Ax^2 + Ay^2). Substitute Ax = -77 cm and Ay = 36 cm into the formula.
Calculate the square of each component: Ax^2 = (-77 cm)^2 and Ay^2 = (36 cm)^2.
Add the squared components: Ax^2 + Ay^2.
Take the square root of the sum to find the magnitude of vector A: |A| = sqrt(Ax^2 + Ay^2).
To find the absolute angle θ of the vector, use the tangent function: θ = arctan(Ay/Ax). Substitute Ay = 36 cm and Ax = -77 cm into the formula and calculate the angle. Adjust the angle based on the quadrant in which the vector lies.
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