Question

A bird is flying south at a rate of

45 miles per hour while being
pushed east by wind with a
speed of 12 miles per hour.
What is the direction of the bird's
resultant vector?
Hint: Draw a vector diagram.
Ө 0 = [ ? ]°
Round your answer to the nearest hundredth.

Answer 1

Explanation:

To determine the direction of the bird's resultant vector, we can use vector addition by considering the bird's southward velocity and the eastward velocity caused by the wind.

Let's represent the southward velocity as a vector "S" with a magnitude of 45 mph and the eastward velocity caused by the wind as a vector "E" with a magnitude of 12 mph.

Using the Pythagorean theorem, the magnitude of the resultant vector can be calculated as follows:

Resultant magnitude = sqrt((Magnitude of S)^2 + (Magnitude of E)^2)

= sqrt((45 mph)^2 + (12 mph)^2)

= sqrt(2025 + 144)

= sqrt(2169)

≈ 46.57 mph

To find the direction, we can use trigonometry. The angle θ can be calculated as:

θ = arctan(Magnitude of E / Magnitude of S)

= arctan(12 / 45)

≈ 14.04°

Rounding to the nearest hundredth, the direction of the bird's resultant vector is approximately 14.04°.