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An object has a force of 150 Newtons applied to it, pushing it towards 140 degrees on the compass. What are the x and y components of this force?

A. 150 sin(140 degrees), 150 cos(140 degrees)
B. 150 sin(40 degrees), 150 cos(40 degrees)
C. 150 sin(140 degrees), 150 sin(140 degrees)
D. 150 cos(140 degrees), 150 cos(140 degrees)

1 Answer

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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)

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