A football player runs the pattern given in the drawing by the three displacement vectors , , and . The magnitudes of these vectors are A = 6.00 m, B = 13.0 m, and C = 15.0 m. Using the component method, find the (a) magnitude and (b)direction of the resultant vector + + . Take to be a positive angle.
Calculate all x components and add
Calculate all y components and add
take sqrt(xtotal^2+ytotal^2)
take tan^-1 (ytotal/xtotal)
To find the magnitude and direction of the resultant vector, we need to add the three displacement vectors, A, B, and C.
First, we need to find the components of each vector. Let's define the x-axis as the horizontal direction and the y-axis as the vertical direction.
The displacement vector A has a magnitude of 6.00 m and an unknown angle, θA. We can find the x-component and y-component of vector A using trigonometry:
Ax = A * cos(θA)
Ay = A * sin(θA)
Similarly, for vector B with a magnitude of 13.0 m and an unknown angle, θB:
Bx = B * cos(θB)
By = B * sin(θB)
And for vector C with a magnitude of 15.0 m and an unknown angle, θC:
Cx = C * cos(θC)
Cy = C * sin(θC)
Now, we can find the components of the resultant vector:
Rx = Ax + Bx + Cx
Ry = Ay + By + Cy
The magnitude of the resultant vector is given by the Pythagorean theorem:
R = sqrt(Rx^2 + Ry^2)
To find the direction, we will use the inverse tangent function:
θR = atan(Ry / Rx)
Substituting the values and solving these equations will give us the magnitude and direction of the resultant vector.