Find the magnitude and direction for the resultant of the three vectors force:F1=(5.0i,-2.5j)N,F3=(-7.5j in)N and F3=(2.5i)N
To find the magnitude and direction of the resultant vector, we can start by adding the three given vectors together to get the resultant vector.
Given vectors:
F1 = (5.0i, -2.5j) N
F2 = (-7.5j) N
F3 = (2.5i) N
To add the vectors, we simply add their corresponding components. Adding the i-components and the j-components separately, we get:
Resultant vector, F_res = (5.0i, -2.5j) + (0i, -7.5j) + (2.5i, 0j) = (5.0i + 2.5i, -2.5j - 7.5j) = (7.5i, -10j)
The magnitude of a vector is given by the formula:
Magnitude = sqrt(i^2 + j^2)
Magnitude of the resultant vector,
Magnitude(F_res) = sqrt((7.5)^2 + (-10)^2) = sqrt(56.25 + 100) = sqrt(156.25) = 12.5
So, the magnitude of the resultant vector is 12.5 N.
To find the direction of the resultant vector, we can use trigonometry. The direction is typically measured counterclockwise from the positive x-axis.
Direction of the resultant vector, θ = arctan(j-component / i-component)
θ = arctan((-10) / 7.5) = arctan(-4/3)
To get a more precise answer, we can convert the angle to degrees or radians using a calculator.
θ ≈ -53.13°
So, the direction of the resultant vector is approximately -53.13° counterclockwise from the positive x-axis.