First, let's break down the given displacements into their horizontal (x) and vertical (y) components. We can use trigonometry to determine these components.
For the displacement of 26 km on a bearing of 175°:
The horizontal component (x) can be found using the cosine function:
x = 26 km * cos(175°)
x ≈ -23.63 km (rounded to two decimal places, as specified by the problem)
The vertical component (y) can be found using the sine function:
y = 26 km * sin(175°)
y ≈ -6.87 km (rounded to two decimal places)
Similarly, for the displacement of 18 km on a bearing of 294°:
The horizontal component (x) can be found using the cosine function:
x = 18 km * cos(294°)
x ≈ 5.46 km (rounded to two decimal places)
The vertical component (y) can be found using the sine function:
y = 18 km * sin(294°)
y ≈ -15.32 km (rounded to two decimal places)
Now, we can add the horizontal and vertical components separately to find the resultant displacement.
Horizontal component: -23.63 km + 5.46 km ≈ -18.17 km (rounded to two decimal places)
Vertical component: -6.87 km + (-15.32 km) ≈ -22.19 km (rounded to two decimal places)
Therefore, the resultant displacement is approximately -18.17 km in the horizontal direction and -22.19 km in the vertical direction.
To represent this graphically, we can draw a Cartesian coordinate system and plot the resultant displacement as a vector with its tail at the origin (0, 0) and its head at (-18.17, -22.19).
