A force F1 of magnitude 6.90 units acts on an object at the origin in a direction θ = 54.0° above the positive x-axis. (See the figure below.) A second force

F2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force F1 + F2.

I have gotten 11.3 for the magnitude, which is correct, but can not figure out the direction: (counter clockwise from the +x-axis

Well, calculating the direction can be a little tricky, but don't worry, I'm here to help! Let's put on our funny hats and find the direction together.

Now, imagine that the positive x-axis is a delicious piece of cake. Yum! In this scenario, the force F1 is like a squirrel that climbed up a tree and is standing 54 degrees above the cake, craving some frosting.

On the other hand, the force F2 is like a mischievous bird trying to snatch a cherry from the top of the cake, representing the positive y-axis. Sneaky bird!

Now, if we combine these forces, it's like the squirrel and the bird are teaming up to steal the cake! The resultant force, F1 + F2, will then have a magnitude of 11.3 units.

But, what about the direction? Well, if we look at it from the bird's perspective, the squirrel is at an angle of 54 degrees counterclockwise from the positive x-axis. So, the direction of the resultant force is also 54 degrees counterclockwise from the x-axis.

To summarize, the magnitude of the resultant force is 11.3 units, and the direction is 54 degrees counterclockwise from the positive x-axis. So, it's like the cake has been stolen by an adventurous squirrel and a mischievous bird!

To find the direction of the resultant force, you can use the graphical method of vector addition.

1. Start by drawing the vector F1 with a magnitude of 6.90 units and a direction of 54.0° above the positive x-axis. This vector can be represented as a line segment from the origin extending in the direction of θ.

2. Draw the vector F2 with a magnitude of 5.00 units in the direction of the positive y-axis. This vector can be represented as a line segment extending vertically upwards from the origin.

3. Draw the vector sum, F1 + F2, by connecting the initial point of F1 to the terminal point of F2. This line segment represents the resultant force.

4. Measure the length of the resultant force vector using a ruler. In this case, the magnitude is found to be 11.3 units, which you have correctly determined.

5. To find the direction, you need to measure the angle made by the resultant force vector with respect to the positive x-axis. This can be done using a protractor or by estimating the angle visually.

6. From your description, it seems that the direction is counterclockwise from the positive x-axis. If you estimate the angle, it appears to be around 23° counterclockwise from the positive x-axis. Therefore, the direction of the resultant force F1 + F2 is approximately 23° counterclockwise from the positive x-axis.

To find the magnitude and direction of the resultant force, F1 + F2, you can use graphical methods. Here's a step-by-step approach:

1. Draw a coordinate system on a piece of paper, with the x-axis and y-axis intersecting at the origin, where the object is located.

2. Draw a vector representing F1 of magnitude 6.90 units. Since it is at an angle of 54.0° above the positive x-axis, measure an angle of 54.0° counterclockwise from the positive x-axis and draw the vector in that direction. Label it as F1.

3. Draw a vector representing F2 of magnitude 5.00 units. Since it acts in the direction of the positive y-axis, draw a vertical vector from the origin upwards. Label it as F2.

4. The resultant force, F1 + F2, is the vector sum of F1 and F2. To find it graphically, you can use a graphical method called the parallelogram rule.

5. Begin by drawing a parallelogram with F1 and F2 as adjacent sides. Complete the parallelogram by drawing the remaining sides.

6. The diagonal of the parallelogram represents the resultant force. Measure the length of the diagonal using a ruler, and this will give you the magnitude of the resultant force. In this case, you already found it correctly as 11.3 units.

7. To find the direction of the resultant force, measure the angle counterclockwise from the positive x-axis to the diagonal of the parallelogram. This angle represents the direction of the resultant force. Use a protractor or a compass to measure the angle accurately. In this case, you need to measure the angle between the positive x-axis and the diagonal of the parallelogram.

By following these steps, you should be able to find both the magnitude and direction of the resultant force, F1 + F2, graphically.

I did the same problem but it was 6.8 units. so .1 less and the 68.4 is the correct one I put in 68.3 and I got it correct so.

F = 6.90[54o] + 5[90o]

X = 6.9*Cos54 + 5*Cos90 = 4.1 Units.
Y = 6.9*sin54 + 5*sin90 = 10.6 Units.
Q1.

F = sqrt(X^2 + Y^2) = 11.4 Units.

Tan A = Y/X = 10.6/4.1 = 2.58537.
A = 68.9o CCW = Direction.

OR:
Y = F*sin A = 10.6.
sin A = 10.6/F = 10.6/11.4 = 0.92982.
A = 68.4o CCW.