What is the resultant of two vectors of 4unit and 5unit acting on a point at an angel 45degree with each other?
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.
To find the resultant of two vectors, you can use the laws of vector addition. We can break down the given vectors into their components and then add them together. The resultant vector can be found by finding the sum of the x-components and the sum of the y-components.
Given:
Vector 1 magnitude: 4 units
Vector 2 magnitude: 5 units
Angle between the vectors: 45 degrees
Step 1: Resolve the vectors into their x and y components.
Vector 1:
Magnitude = 4 units
Component along x-axis = 4 * cos(45°) = 4 * √(2)/2 = 2√(2) units
Component along y-axis = 4 * sin(45°) = 4 * √(2)/2 = 2√(2) units
Vector 2:
Magnitude = 5 units
Component along x-axis = 5 * cos(45°) = 5 * √(2)/2 = 5√(2)/2 units
Component along y-axis = 5 * sin(45°) = 5 * √(2)/2 = 5√(2)/2 units
Step 2: Add the x-components and y-components separately.
Sum of x-components = 2√(2) + 5√(2)/2 = (4 + 5)/√(2) units = 9√(2)/2 units
Sum of y-components = 2√(2) + 5√(2)/2 = (4 + 5)/√(2) units = 9√(2)/2 units
Step 3: Combine the x-component sum and y-component sum to form the resultant vector.
Resultant vector = (√(2)/2) * (9√(2)/2) units + (√(2)/2) * (9√(2)/2) units
= (9 * 2)/4 + (9 * 2)/4 units
= 18/4 + 18/4 units
= 9/2 + 9/2 units
= 9 + 9/2 units
= 18/2 + 9/2 units
= 27/2 units
Therefore, the resultant of the two vectors with magnitudes of 4 units and 5 units, acting at an angle of 45 degrees, is 27/2 units.
To find the resultant of two vectors acting on a point at an angle, you can use the concept of vector addition. Here are the steps to find the resultant:
1. Start by drawing the two vectors on a coordinate system. Let's call the first vector "A" with a magnitude of 4 units and the second vector "B" with a magnitude of 5 units.
2. Since the vectors are acting at an angle of 45 degrees with each other, draw the vectors such that they form a 45-degree angle when measured from the tail of the first vector to the head of the second vector.
3. To find the resultant, you need to add the two vectors together. This can be done by splitting each vector into its horizontal and vertical components.
4. Calculate the horizontal component of vector A by multiplying its magnitude (4 units) by the cosine of the angle (45 degrees). Similarly, calculate the vertical component of vector A by multiplying its magnitude by the sine of the angle.
Horizontal component of A = 4 units * cos(45 degrees)
Vertical component of A = 4 units * sin(45 degrees)
5. Repeat step 4 for vector B.
Horizontal component of B = 5 units * cos(45 degrees) = 5 units * (√2/2)
Vertical component of B = 5 units * sin(45 degrees) = 5 units * (√2/2)
6. Add the horizontal components of both vectors together to find the horizontal component of the resultant. Similarly, add the vertical components to find the vertical component of the resultant.
Horizontal component of resultant = Horizontal component of A + Horizontal component of B
Vertical component of resultant = Vertical component of A + Vertical component of B
7. Finally, use the Pythagorean theorem to find the magnitude of the resultant vector. The magnitude is the square root of the sum of the squares of the horizontal and vertical components.
Magnitude of the resultant = sqrt((Horizontal component of resultant)^2 + (Vertical component of resultant)^2)
By following these steps and performing the calculations, you can find the magnitude and direction (angle) of the resultant vector.