If a man travels 5km 40 degree west of north then 8km east find the resultant displacement
All angles are measured CCW from +x-axis.
Disp. = 5km[130o] + 8km[0o].
X = 5*Cos130 + 8*Cos0 = -3.21 + 8 = 4.79 km.
Y = 5*sin130 + 8*sin0 = 3.83 km.
Disp. = 4.79 + 3.83i = 6.13 km[38.6o].
To find the resultant displacement, we need to consider the horizontal and vertical components of the man's travel separately and then combine them to get the final displacement.
First, let's consider the 5 km travel 40 degrees west of north. This means the man is moving in a diagonal direction, making an angle of 40 degrees with the vertical north direction.
We can break down the 5 km travel into its horizontal and vertical components using trigonometry. The horizontal component is given by:
Horizontal component = 5 km * cos(40 degrees)
Similarly, the vertical component is given by:
Vertical component = 5 km * sin(40 degrees)
Now, let's consider the 8 km travel east. Since this travel is purely horizontal, it does not have a vertical component.
The horizontal component of this travel is simply 8 km.
To find the resultant displacement, we need to add the horizontal and vertical components separately, taking into account their directions.
Horizontal displacement = 8 km - Horizontal component (5 km * cos(40 degrees))
Vertical displacement = Vertical component (5 km * sin(40 degrees))
Final resultant displacement = Square root of [(Horizontal displacement)^2 + (Vertical displacement)^2]
Now, we can substitute the values and calculate the resultant displacement.