To find the resultant of two vectors, you can use the parallelogram law of vector addition. This law states that the resultant of two vectors can be found by drawing a parallelogram with the vectors as adjacent sides and the diagonal of the parallelogram represents the resultant.
In this case, you have two vectors of 4 units and 5 units acting at an angle of 45 degrees with each other.
First, draw the two vectors as adjacent sides of a parallelogram. At one of the vectors' starting point, draw a line at a 45-degree angle. This line represents the other vector.
Using a ruler, measure and draw the vectors. The first vector (4 units) can be represented as follows:
|
|_____________4 units
|
Now, draw the second vector (5 units) originating from the same starting point, but at a 45-degree angle:
|\
| \__________5 units
|
Now, complete the parallelogram by drawing the other two sides:
|\
| \
|____\_____
\
The diagonal of the parallelogram represents the resultant vector. Measure the length of the diagonal and that would give the magnitude of the resultant vector.
The magnitude of the resultant vector can be found using the Law of Cosines:
c^2 = a^2 + b^2 - 2ab*cos(C)
Where:
c is the length of the diagonal (resultant vector)
a and b are the lengths of the two vectors (4 units and 5 units)
C is the angle between the two vectors (45 degrees)
Using the formula, substitute the values:
c^2 = 4^2 + 5^2 - 2(4)(5) * cos(45 degrees)
c^2 = 16 + 25 - 40 * cos(45 degrees)
c^2 = 41 - 40 * sqrt(2)/2
c^2 ≈ 41 - 40 * 0.7071
c^2 ≈ 41 - 28.284
c^2 ≈ 12.716
c ≈ √12.716
c ≈ 3.57 units
Therefore, the magnitude of the resultant vector is approximately 3.57 units.
what is the resultant of two vectors of 4unit and 5unit acting on an angel 45 degree with each other ?
1 answer
1 answer