Question

Three workers move a car by pulling on three ropes. The first worker exerts a force of 600 N to the north, the second a force of 752 N to the east, and the third 675 N at 30.0° south of east. In what precise direction does the car move?

Answer 1

The car will move east-northeast with a resultant force of approximately 1229 N to the east and 1156 N to the north.

Step-by-step explanation:

The car will move in the direction determined by the resultant of the forces applied by the workers. To find the resultant, we can break down the forces into their x and y components and then add them up.

For the first worker, the force is 600 N to the north, which means it has no horizontal component. For the second worker, the force is 752 N to the east, which means it has no vertical component. For the third worker, the force is 675 N at 30.0° south of east. This can be broken down into a vertical component of 675 N * cos(30°) and a horizontal component of 675 N * sin(30°).

Adding up all the horizontal forces gives us 752 N + 675 N * sin(30°), which is approximately 1229 N to the east. Adding up all the vertical forces gives us 600 N + 675 N * cos(30°), which is approximately 1156 N to the north.

Therefore, the car will move approximately east-northeast with a resultant force of approximately 1229 N to the east and 1156 N to the north.