Question

The velocity of a polar bear is given by vector u = (-20.6 km/h, -12.6 km/h).

A) How fast is the polar bear moving, in km/h?
B) In what direction is the polar bear moving? Express your answer as an angle measured in degrees below the negative x-axis.

Answer 1

Calculate the magnitude of the velocity vector to determine the polar bear's speed. The direction is found by calculating the arctangent of the ratio of the y-component to the x-component and expressing it in degrees.

Step-by-step explanation:

The question asks how fast the polar bear is moving and in what direction, given its velocity vector u = (-20.6 km/h, -12.6 km/h). To find the speed of the polar bear, we calculate the magnitude of the velocity vector:

v = √((-20.6 km/h)² + (-12.6 km/h)²)

For the direction, we seek the angle relative to the negative x-axis. Thus, we compute the arctangent of the ratio of the y-component to the x-component of the vector and convert it into degrees:

θ = tan⁻¹(-12.6 / -20.6)

The speed is the scalar magnitude of the velocity vector, and the direction can be described relative to a specified axis, providing a clear example of vector components and their geometric interpretation.