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.
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.