To solve this problem, we can use the fact that the resultant vector is the sum of vectors A and B.
a) The horizontal component of vector A is given by A_x = A * cosθ = 4 * cos(30°). Since vector B is directed along the positive x-axis, its horizontal component is equal to its magnitude, B_x = 4. Therefore, the horizontal component of the resultant vector is A_x + B_x = 4 * cos(30°) + 4.
b) The vertical component of vector A is given by A_y = A * sinθ = 4 * sin(30°) = 2. Since vector B is directed along the positive x-axis, its vertical component is zero, B_y = 0. Therefore, the vertical component of the resultant vector is A_y + B_y = 2.
c) The magnitude of the resultant vector is given by R = sqrt(R_x^2 + R_y^2), where R_x is the horizontal component and R_y is the vertical component of the resultant vector. Plugging in the values we've found, R = sqrt((4 * cos(30°) + 4)^2 + 2^2).
d) The direction of the resultant vector can be found using the inverse tangent function. The angle θ between the positive x-axis and the resultant vector is given by tanθ = R_y / R_x. Solving for θ, θ = atan(R_y / R_x).
Now, you can calculate the values for a), b), c), and d) using the given formulas and the values provided.
5. Vector à has magnitude of 4 units and makes an angle of 30° with the positive x-axis.
B Vector also has the same magnitude of 4 units and directed along the positive x-axis
Calculate:
a) the horizontal component of the resultant vector,
b) vertical component of the resultant vector,
c) the magnitude of the resultant vector,
d) the direction of the resultant vector.
1 answer