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

To determine the direction of the bird's resultant vector, we can use vector addition. Drawing a vector diagram will help visualize the situation.

Let's consider the bird's southward velocity as one vector and the eastward velocity due to the wind as another vector. We can represent the southward velocity with a vector pointing downward and labeled as 45 mph. The eastward velocity due to the wind can be represented by a vector pointing to the right and labeled as 12 mph.

Now, to find the resultant vector, we can draw a vector that connects the tail of the first vector (southward velocity) to the head of the second vector (eastward velocity due to wind). The resultant vector represents the combined effect of both velocities.

Using the Pythagorean theorem, we can calculate the magnitude of the resultant vector:

Resultant magnitude = √(45^2 + 12^2) ≈ 47.54 mph

Next, we can determine the direction of the resultant vector using trigonometry. The angle (Ө) between the resultant vector and the southward direction can be found using the inverse tangent:

Ө = arctan(12/45) ≈ 15.95°

Rounding to the nearest hundredth, the direction of the bird's resultant vector is approximately 15.95° south of due east.