Question

What is the resultant of two vectors of 4unit and 5unit acting on a point at an angel 45degree with each other?

Answer 1

To find the resultant of two vectors, we can use the vector addition method.

Let's denote the two vectors as A and B, where A has a magnitude of 4 units and B has a magnitude of 5 units.

Since the vectors are at an angle of 45 degrees with each other, we can form a right triangle.

Using trigonometry, we can determine the components of the vectors.

The x-component of vector A is A * cos(45) = 4 * cos(45) = 2.828 units
The y-component of vector A is A * sin(45) = 4 * sin(45) = 2.828 units

The x-component of vector B is B * cos(45) = 5 * cos(45) = 3.536 units
The y-component of vector B is B * sin(45) = 5 * sin(45) = 3.536 units

To find the resultant vector, we add the x-components and the y-components separately.

Resultant x-component: 2.828 + 3.536 = 6.364 units
Resultant y-component: 2.828 + 3.536 = 6.364 units

We can now use the Pythagorean theorem to find the magnitude of the resultant vector.

Resultant magnitude = sqrt((Resultant x-component)^2 + (Resultant y-component)^2)
= sqrt((6.364)^2 + (6.364)^2)
= sqrt(40.424 + 40.424)
= sqrt(80.848)
= 8.999 units (rounded to three decimal places)

Therefore, the resultant of the two vectors with magnitudes of 4 units and 5 units acting at an angle of 45 degrees with each other is approximately 8.999 units.