Question

If the velocity vector of a polar bear is →u=(−18.0ˆi−13.0ˆj)km/h, how fast and in what geographic direction is it heading? Here, ˆi and ˆj are directions to geographic east and north, respectively.

a) 22.8 km/h, 37.38° north of east
b) 23.4 km/h, 53.13° south of east
c) 20.4 km/h, 24.46° west of north
d) 19.7 km/h, 65.42° east of north

Answer 1

The polar bear is moving at a speed of approximately 22.18 km/h in a direction approximately 36.87° north of east.

Step-by-step explanation:

To find the speed and direction of the polar bear's motion, we can use the Pythagorean theorem to calculate the magnitude of the velocity vector. The magnitude of the velocity vector is given by the formula: |→u|= √((−18.0)^2 + (−13.0)^2).

Substituting the values, we get: |→u|= √(324 + 169) = √493 ≈ 22.18 km/h.

The direction of the velocity can be found using the inverse tangent function. The direction angle θ is given by the formula: θ = tan^−1(−13.0/−18.0).

Substituting the values, we get: θ = tan^−1(13/18) ≈ 36.87° north of east.