Question

5. Vector à has magnitude of 4 units and makes an angle of 30° with the positive x-axis.
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.

Answer 1

a) The horizontal component of the first vector can be found using the formula:

Horizontal component = magnitude × cos(angle)

Substituting the values given, we get:

Horizontal component = 4 × cos(30°)
= 4 × √3/2
= 2√3 units

b) Since the first vector is parallel to the x-axis, the vertical component is zero.

Vertical component = 0 units

c) The magnitude of the resultant vector can be found using the Pythagorean theorem:

Magnitude of resultant vector = √(horizontal component)^2 + (vertical component)^2
= √((2√3)^2 + 0^2)
= √(12 + 0)
= √12
= 2√3 units

d) The direction of the resultant vector can be found using the inverse tangent function:

Direction = arctan(vertical component / horizontal component)
= arctan(0 / (2√3))
= arctan(0)
= 0°

Therefore, the direction of the resultant vector is 0° with the positive x-axis.