Choose the one alternative that best completes the statement or answers the question.
-Two forces of magnitude 25 pounds and 40 pounds act on an object. The force of $40 \mathrm { lb }$ acts along the positive $\mathrm { x }$-axis, and the force of $25 \mathrm { lb }$ acts at an angle of $80 ^ { \circ }$ with the positive $x$-axis. Find the direction and magnitude of the resultant force. Round the direction and magnitude to the nearest whole number.
A) Direction: $40 ^ { \circ }$; magnitude: $47 \mathrm { lb }$
B) Direction: $51 ^ { \circ }$; magnitude: $51 \mathrm { lb }$
C) Direction: 29°; magnitude: $51 \mathrm { lb }$
D) Direction: $4 ^ { \circ }$; magnitude: $65 \mathrm { lb }$

Question

Quizplus · Accepted Answer

The resultant force can be calculated using vector addition. The x-component is $40 + 25 \cos(80^\circ)$ and the y-component is $25 \sin(80^\circ)$. The magnitude is approximately 51 lb, and the direction is approximately 29°.

Choose the One Alternative That Best Completes the Statement or Answers