Two rugby players, A and B, start running from the same point on the pitch. Player A runs 20 m towards the South, then turns to his left and runs 26 m. Meanwhile, Player B runs 12 m towards the West, then 6 m towards the South, and then turns to his left and runs 38 m. Where is Player A now located with respect to Player B?

Introduction / Context:
In this question, two rugby players move on the same field along different routes, and we are asked to find the relative position of Player A with respect to Player B at the end. This is a typical direction sense and relative position problem. Instead of focusing on where each player is relative to the origin, we specifically compare their final coordinates to see whether A is North, South, East or West of B and by what distance.

Given Data / Assumptions:

• Both Player A and Player B start from the same point on the pitch.
• Player A runs 20 m towards the South and then turns left to run 26 m.
• Player B runs 12 m towards the West, then 6 m towards the South, and then turns left to run 38 m.
• All turns are right-angle turns, and all distances are straight-line segments.
• We use the standard convention: from South, a left turn faces East, and from West, a left turn faces South.
• We choose a coordinate system with North–South as the vertical axis and East–West as the horizontal axis.

Concept / Approach:
To solve this systematically, we assign coordinates to each final position. We place the common starting point at (0, 0). Vertical movements change the y-coordinate (positive for North, negative for South), while horizontal movements change the x-coordinate (positive for East, negative for West). After computing the final coordinates of both players, we compare them. If Player A has a smaller y-coordinate than Player B but the same x-coordinate, A will be directly South of B by the difference in their y-values.

Step-by-Step Solution:
Step 1: Let the starting point of both players be (0, 0). Step 2: Track Player A. He runs 20 m South, reaching (0, -20). Step 3: From facing South, a left turn means facing East. Running 26 m East, he reaches (26, -20). So Player A's final coordinates are (26, -20). Step 4: Track Player B. He first runs 12 m West, reaching (-12, 0). Step 5: Next, he runs 6 m South to reach (-12, -6). Step 6: From facing South, a left turn means facing East. Running 38 m East from (-12, -6) takes him to (-12 + 38, -6) = (26, -6). So Player B's final coordinates are (26, -6). Step 7: Compare the positions: A is at (26, -20) and B is at (26, -6). They have the same x-coordinate (26), so they are vertically aligned. A's y-coordinate is -20, while B's is -6, which is 14 units higher. Therefore, Player A is 14 m South of Player B.

Verification / Alternative check:
We can also reason qualitatively. Both players eventually end up on the same vertical line because Player A moves East 26 m and Player B net moves West 12 m and then East 38 m, which results in 26 m East of the origin. For vertical movement, A goes 20 m South, whereas B effectively goes only 6 m South, so A is 14 m further South than B (20 − 6 = 14). This confirms that A is directly South of B by 14 m, matching the coordinate-based calculation.

Why Other Options Are Wrong:
26 m South or 26 m North are incorrect magnitudes; 26 m is the horizontal distance from the starting point, not the vertical separation between the players. 14 m North of B would reverse the direction; instead of A being above B, we found that A is lower (more South). 38 m East is unrelated to the vertical question being asked and simply reflects one of the segments run by B, not the relative position between A and B.

Common Pitfalls:
One common error is ignoring the sign of the vertical displacement and assuming that the larger raw number corresponds to the correct answer. Another is confusing left and right turns or mixing up which player made which move, which leads to incorrect coordinates. Writing down each intermediate point and carefully computing the net displacements is a robust way to avoid such mistakes. A simple sketch of the field with axes and labelled points for A and B also makes the relative position very clear.

Final Answer:
Player A is located 14 m South of Player B.