C

Step 1: Understand the concept of velocity change. Velocity is a vector quantity that has both magnitude and direction.
Step 2: The initial velocity of the truck when it's traveling due north is given as 20 m/s. We can represent this initial velocity vector as:
\( ext{V}_{i} = 20 ext{ m/s} ext{ in the North direction} \)
Step 3: When the truck turns west and continues to travel at the same speed, its new velocity can be represented as:
\( ext{V}_{f} = 20 ext{ m/s} ext{ in the West direction} \)
Step 4: To calculate the change in velocity (\( ext{ΔV} \)), we need to subtract the initial velocity vector from the final velocity vector.
The initial velocity vector \( ext{V}_{i} \) can be represented as:
\( ext{V}_{i} = (0, 20) \)
where the first component is the east-west direction (0 m/s for east) and the second component is the north-south direction (20 m/s for north).
The final velocity vector \( ext{V}_{f} \) can be represented as:
\( ext{V}_{f} = (-20, 0) \)
Step 5: Now, we calculate the change in velocity:
\( ext{ΔV} = ext{V}_{f} - ext{V}_{i} = (-20, 0) - (0, 20) \)
\( ext{ΔV} = (-20, -20) \)
Step 6: Now, to find the magnitude of the change in velocity, we use the Pythagorean theorem:
\( | ext{ΔV}| = \sqrt{(-20)^2 + (-20)^2} = \sqrt{400 + 400} = \sqrt{800} = 20\sqrt{2} \text{ m/s} \)
Therefore, the change in velocity is \( 20\sqrt{2} \text{ m/s} \) or approximately 28.28 m/s.