Final answer:
The polar bear is moving at a speed of approximately 22.85 km/h in a direction approximately 37 degrees below the negative x-axis.
Step-by-step explanation:
The velocity of a polar bear is given by the vector u = (-18.2 km/h, -13.8 km/h). To determine how fast the polar bear is moving, we need to calculate the magnitude of its velocity vector.
To find the magnitude (v), which represents the polar bear's speed, we use the Pythagorean theorem:
v = √((-18.2)^2 + (-13.8)^2) km/h
v = √(331.24 + 190.44) km/h
v = √521.68 km/h
v = 22.85 km/h approximately
So, the polar bear is moving at 22.85 km/h.
To determine the direction of the polar bear's movement, we calculate the angle with respect to the negative x-axis. This angle (θ) can be found using the tangent function:
θ = tan-1(-13.8 / -18.2)
It corresponds to an angle below the negative x-axis, which can be calculated as follows:
θ = tan-1(0.75824)
θ = 37 degrees approximately
The polar bear is moving in a direction that is approximately 37 degrees below the negative x-axis.