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:
- Drawing a Cartesian coordinate system.
- Determining the scale to use (example: 1 cm=10 km).
- Adding the vectors by drawing them tip-to-tail using a ruler and protractor.
- Labeling each vector with the appropriate letter, magnitude, and angle.
- 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:
- Calculating the x and y-components of each vector.
- Finding the x-component and y-component of the resultant vector.
- Calculating the magnitude of the resultant vector.
- 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!