Given two vectors 5N at 0 degrees and 5N at 180 degrees, calculate the resultant vector.
Understand the Problem
The question is asking for the calculation of the resultant vector from two given vectors, one pointing at 0 degrees with a magnitude of 5N and the other pointing at 180 degrees also with a magnitude of 5N. This involves vector addition taking into account their directions.
Answer
The resultant vector is $0N$.
Answer for screen readers
The resultant vector has a magnitude of $0N$ and an undefined direction.
Steps to Solve
- Identify the components of each vector
For vector A, which is at 0 degrees (along the positive x-axis), the components can be calculated as:
- ( A_x = 5N \cdot \cos(0^\circ) = 5N )
- ( A_y = 5N \cdot \sin(0^\circ) = 0N )
For vector B, which is at 180 degrees (along the negative x-axis), the components are:
- ( B_x = 5N \cdot \cos(180^\circ) = -5N )
- ( B_y = 5N \cdot \sin(180^\circ) = 0N )
- Add the components of the vectors
Now, we can find the resultant vector components by adding the respective components:
- ( R_x = A_x + B_x = 5N + (-5N) = 0N )
- ( R_y = A_y + B_y = 0N + 0N = 0N )
- Calculate the magnitude of the resultant vector
The magnitude of the resultant vector ( R ) is given by: $$ R = \sqrt{R_x^2 + R_y^2} $$ Substituting the values we calculated: $$ R = \sqrt{0N^2 + 0N^2} = \sqrt{0} = 0N $$
- Determine the direction of the resultant vector
Since both components ( R_x ) and ( R_y ) are zero, the direction is undefined, indicating that the resultant vector is a zero vector.
The resultant vector has a magnitude of $0N$ and an undefined direction.
More Information
When two equal vectors point in exactly opposite directions, they completely cancel each other out, resulting in a zero vector. This scenario can often occur in physics, particularly when balancing forces.
Tips
- Forgetting to include direction: When adding vectors, always consider their direction and ensure you're using the correct angle for calculations.
- Mistakenly believing the resultant can be non-zero: If two vectors are equal in magnitude and opposite in direction, the resultant will always be zero.
