How to Calculate Displacement Vector: A Fun Physics Experiment

How can we calculate the displacement vector of a plane's journey?

Let's find out how to solve this physics problem step by step!

Step-by-Step Solution:

Now, let's walk through the process of calculating the displacement vector of the plane's journey:

Firstly, we need to assign a letter (\"A\", \"B\", \"C\", etc.) to each vector and record their magnitudes and angles.

Vector | Magnitude (km) | Angle (degrees)

------- | -------- | --------

A | 40 | 0

B | 30 | 15

C | 50 | -30

Next, we write an addition equation for our vectors: R = A + B + C

Then, we find the resultant vector graphically by:

1. Drawing a Cartesian coordinate system.
2. Determining the scale to use (example: 1 cm=10 km).
3. Adding the vectors by drawing them tip-to-tail using a ruler and protractor.
4. Labeling each vector with the appropriate letter, magnitude, and angle.
5. Drawing the resultant vector and determining its magnitude and angle.

The resultant vector is calculated to be:

Magnitude = 68.2 km

Angle = -18.2 degrees

After that, we find the resultant vector analytically by:

1. Calculating the x and y-components of each vector.
2. Finding the x-component and y-component of the resultant vector.
3. Calculating the magnitude of the resultant vector.
4. Determining the angle of the resultant vector with respect to the x-axis.

The analytical calculation yields the same result:

Magnitude = 68.2 km

Angle = -18.2 degrees

Finally, we calculate the % difference between the graphical and analytical results (0%) and compare the angles (measured vs. calculated).

The measured angle and calculated angle are both -18.2 degrees, showing equality.

This fun physics experiment helps us understand how to calculate displacement vectors accurately!