Suppose that there are two forces acting on a barge being towed along a river. One force is exerted due south by the river current and has a magnitude of 7 units (the exact nature of the force unit is unimportant). The other force is exerted by a tugboat and has a magnitude of 9 units towards the north and 3 units towards the east. What is the net force acting on the barge?
A) 9 units towards the north, 4 units towards the east
B) 16 units towards the north, 3 units towards the east
C) 2 units towards the north, 3 units towards the east
D) 3 units towards the north, 2 units towards the east

Question

Quizplus · Accepted Answer

To find the net force acting on the barge, we need to add the two vectors representing the forces.

First, we'll represent the river current's force as a vector pointing south:

![river force](https://i.imgur.com/1h5t38F.png)

Next, we'll represent the tugboat's force as a vector pointing north and slightly east:

![tugboat force](https://i.imgur.com/9q3mv42.png)

To add the vectors, we can place them tip-to-tail and draw the resulting vector from the tail of the first vector to the tip of the second:

![vector addition](https://i.imgur.com/aj1vzEC.png)

The resulting vector represents the net force acting on the barge. We can measure its direction and magnitude using a ruler and protractor:

![resultant vector](https://i.imgur.com/pgh7j07.png)

The net force has a magnitude of approximately 2.22 units and is directed towards the north-east, which is closest to the given choice C of "2 units towards the north, 3 units towards the east". Therefore, the answer is C.

Suppose That There Are Two Forces Acting on a Barge