Understanding Morning Shadows and Directions

This question involves understanding how shadows are cast in the morning and using that information to determine a person's facing direction based on their relative position.

Let's break down the problem step-by-step:

Shadow Direction in the Morning

The direction of a shadow is determined by the position of the sun. In the morning, the sun rises in the East. Therefore, any object will cast a shadow directly opposite to the sun's position, which is towards the West.

• Sun's position in the morning: East
• Shadow direction in the morning: West

Analyzing the Meeting Point

The problem states that when X and Y meet, Y's shadow falls upon X.

• Y's shadow is falling towards the West.
• The fact that Y's shadow falls upon X means that X is located where Y's shadow is being cast.
• Therefore, X is positioned to the West of Y at the meeting point.

We can visualize this:

Since Y's shadow is to Y's West and X is in Y's shadow, X is to the West of Y.

Determining X's Facing Direction

X and Y are walking towards each other. When they meet, X is to the West of Y. For X to meet Y, X must have been walking towards Y's initial position (or towards Y's current position relative to X at the meeting point).

• At the moment of meeting, X is to the West of Y.
• This means Y is to the East of X.
• Since X and Y walked towards each other, X must have been walking in the direction of Y.
• Therefore, X must have been walking and facing towards the East to meet Y, who was located to X's East.

Let's summarize the logic:

• Morning means shadows point West.
• Y's shadow on X means X is West of Y at the meeting point.
• For X to meet Y, X must walk towards Y.
• If Y is East of X (because X is West of Y), X must walk East.
• So, X was facing East.

Conclusion

Based on the analysis of shadow direction in the morning and the relative positions of X and Y when they meet, we can determine X's facing direction.

In the morning, shadows fall West. If Y's shadow falls on X, X is to the West of Y. To walk towards Y, who is to the East, X must be facing East.

Therefore, X was facing East.

Revision Table: Morning Shadow Concepts

Additional Information on Direction and Relative Position

Understanding relative position is key in these types of problems. When we say "A is to the North of B", it means if you were standing at B, you would look North to see A.

Similarly, when we deduced that "X is to the West of Y" because Y's shadow (which is West of Y) falls on X, it means if you were at Y's position, looking West, you would see X.

Conversely, if X is to the West of Y, then Y must be to the East of X. If X was walking towards Y, X must be facing East.

These directional problems often require combining knowledge of celestial mechanics (sun's position) with relative positioning and movement.