A force vector F1 points due east and has a magnitude of 200 newtons. A second force F2 is added to F1. The resultant of the two vectors has a magnitude of 400 newtons and points along the east/west line. Find the magnitude and direction of F2. Note that there are two answers.

Question

A force vector F1 points due east and has a magnitude of 200 newtons. A second force F2 is added to F1. The resultant of the two vectors has a magnitude of 400 newtons and points along the east/west line. Find the magnitude and direction of F2. Note that there are two answers.

i don't get the question, what it means by "points along the east/west line",how come it would has two answers?

PLZ HELPPPPPPPPPPP, THANKS A LOT!!!!

Answer 1

The question is asking us to find the magnitude and direction of the second force vector, F2, when it is added to the first force vector, F1, resulting in a resultant vector with a magnitude of 400 newtons that points along the east/west line.

To solve this problem, we can use vector addition. The magnitude of the resultant vector is equal to the sum of the magnitudes of the individual vectors being added. In this case, the magnitudes of F1 and F2 add up to 400 newtons.

Given that F1 has a magnitude of 200 newtons and the resultant vector has a magnitude of 400 newtons, we can deduce that the magnitude of F2 is 400 - 200 = 200 newtons.

Now let's consider the direction of F2. Since the resultant vector points along the east/west line, we can conclude that F2 must have a direction that is opposite to F1. This means that F2 points due west. However, keep in mind that the question mentions there are two answers. This is because there are two ways in which F2 can be directed due west while still resulting in a magnitude of 200 newtons.

So, the two possible answers are:
1. F2 has a magnitude of 200 newtons and points due west.
2. F2 has a magnitude of 200 newtons and points due west, but in the opposite direction compared to the first answer.

I hope this explanation clears up any confusion. Let me know if you have any further questions!

Answer 2

The question states that the resultant of the two vectors has a magnitude of 400 newtons and points along the east/west line. This means that the resultant force is solely in the east or west direction, with no component in the north or south direction.

To determine the magnitude and direction of F2, we can use vector addition. Let's assume that F2 has a magnitude of x newtons and makes an angle of θ with respect to the east direction.

Using vector addition, we can write the equation:

F1 + F2 = Resultant

Since F1 points due east, it can be written as:

F1 = 200 N (due east)

The magnitude of the resultant is given as 400 newtons, so we can write:

200 + x = 400

Solving for x, we find:

x = 400 - 200 = 200 N

Therefore, one possible magnitude for F2 is 200 newtons.

Now, let's consider the direction. Since the resultant points along the east/west line, the angle θ can be either 0° or 180°. In other words, F2 can point either due east or due west.

So, the two possible answers are:

1) Magnitude of F2 = 200 newtons, direction of F2 = due east
2) Magnitude of F2 = 200 newtons, direction of F2 = due west

These are the two possible solutions for F2 that satisfy the given conditions.

Answer 3

I will give you one hint....

F1+F2=+-400E
F1=100E
solve for F2.