Question
What is the resultant of two vectors of 4unit and 5unit acting on a point at an angel 45degree with each other?
Answers
Answered by
GPT 3.5
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.
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.