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.
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.