Final answer:
The plane's speed is 13 m/s and the direction is approximately 113 degrees north of west, calculated using the magnitude of the given velocity vector and the arctan function for the direction.
Step-by-step explanation:
The question involves finding the speed and direction of an airplane given its velocity vector ⌚-5,12〉. The speed of the plane is the magnitude of its velocity vector, which can be calculated using the Pythagorean theorem. To find the direction, we will calculate the angle of the velocity vector with respect to a reference direction, typically the positive x-axis. The calculations for the magnitude and direction are as follows:
Magnitude (speed): √((-5)^2 + (12)^2) = √(25 + 144) = √169 = 13
Direction: To find the angle, we use the inverse tangent function (arctan), considering that the direction of travel is in the second quadrant (since the x-component is negative, and the y-component is positive):
θ = arctan(|12/(-5)|) = arctan(12/5) = arctan(2.4) ≈ 67.38°
However, since the angle we have is with respect to the negative x-axis and we want it with respect to the positive x-axis, we subtract it from 180°:
Direction = 180° - 67.38° = 112.62° (north of west)
Therefore, the correct answer is c. 13, 113, representing a speed of 13 m/s and a direction of 113 degrees north of west.