Two trucks, A and B, start from the same warehouse. Truck A goes 6 kilometres towards the north and then turns to its right and goes 4 kilometres. Meanwhile, truck B goes 9 kilometres towards the east, then turns towards the north and goes 6 kilometres, and then turns to its right and goes 4 kilometres. Where is truck B located with respect to truck A?

Introduction / Context:
This is a relative position problem with two moving objects, trucks A and B, starting from the same warehouse but following different routes. The goal is to track the final coordinates of each truck and then compute the displacement of truck B with respect to truck A. Problems of this type test a student's ability to apply coordinate reasoning to multiple moving entities at the same time.

Given Data / Assumptions:

• Both trucks start from the same warehouse, treated as the origin.
• Truck A goes 6 kilometres north, then turns right and goes 4 kilometres.
• Truck B goes 9 kilometres east, then 6 kilometres north, and then 4 kilometres to its right from that direction.
• All turns are right angle turns.
• We must find the position of truck B relative to truck A, that is, where B is located with respect to A.

Concept / Approach:
We use the coordinate system where east is positive x, north is positive y, west negative x and south negative y. We first find the final coordinates of truck A, then the final coordinates of truck B. To get the position of B with respect to A, we subtract A's coordinates from B's coordinates. The direction and distance of this difference vector tell us the required relative location.

Step-by-Step Solution:
Step 1: Place the warehouse at (0, 0). Step 2: For truck A, going 6 kilometres north moves it to (0, 6). Step 3: From facing north, a right turn leads east. Moving 4 kilometres east takes truck A to (4, 6). This is the final position of truck A. Step 4: For truck B, going 9 kilometres east moves it to (9, 0). Step 5: From facing east, turning towards the north and going 6 kilometres takes truck B to (9, 6). Step 6: From facing north, a right turn leads east. Moving 4 kilometres east moves truck B to (13, 6). This is the final position of truck B. Step 7: Now we find the displacement of B with respect to A by subtracting A's coordinates from B's coordinates: (13, 6) minus (4, 6) equals (9, 0). Step 8: A difference of (9, 0) means truck B is 9 kilometres east of truck A.

Verification / Alternative check:
We can think qualitatively. Both trucks eventually reach the same northward level (y coordinate 6 kilometres north of the warehouse), because truck A goes up 6 kilometres and truck B also goes up 6 kilometres after its eastward movement. Horizontally, truck A ends 4 kilometres east of the warehouse, while truck B ends 13 kilometres east (9 plus another 4). Differences in eastward distances are therefore 13 minus 4 = 9 kilometres. Since there is no difference in their north-south positions, B must be exactly 9 kilometres east of A.

Why Other Options Are Wrong:

• Option A, 17 kilometres East, incorrectly adds some distances without tracking coordinates precisely.
• Option B, 9 kilometres West, has the correct magnitude but the wrong direction, reversing east and west.
• Option C, 17 kilometres West, is incorrect both in magnitude and direction.
• Option E, 5 kilometres East, is an underestimation that does not match the computed coordinate difference.

Common Pitfalls:
A common mistake is to subtract the wrong coordinates or to neglect that both trucks end up at the same vertical level. Some learners also confuse the relative phrase "with respect to truck A" and instead compute the position of A from B. Always verify the relative direction by picturing A at its final point and visualising how far and in which direction one must travel to reach B.

Final Answer:
Truck B is located 9 kilometres East of truck A.