Final answer:
The x and y components of a 150 Newton force applied at 140 degrees on the compass are calculated using trigonometric functions: 150 cos(140 degrees) for the x-component and 150 sin(140 degrees) for the y-component.
Step-by-step explanation:
The calculation of the x and y components of a force based on its angle from a compass direction involves trigonometric functions. For a force of 150 Newtons applied at 140 degrees on the compass:
- The x-component (horizontal) is found using the cosine function of the angle because it represents the adjacent side of the right triangle formed on the x-axis. In this case, it's negative because 140 degrees lies in the second quadrant of the Cartesian plane where cosine values are negative.
- The y-component (vertical) is determined using the sine function of the angle because it corresponds to the opposite side of the right triangle formed on the y-axis. Similar to the x-component, it's also negative in the second quadrant due to the direction of the force.
Hence, the correct components of the force are:
- x-component: 150 cos(140 degrees)
- y-component: 150 sin(140 degrees)
Therefore, the correct answer to the student's question is: A. 150 sin(140 degrees), 150 cos(140 degrees)