The problem provided involves analyzing displacement-time graphs for the vertical and horizontal components of motion when an object is thrown horizontally from a building.

Key points to consider:

• Horizontal Motion: The horizontal velocity remains constant (since there is no air resistance), and thus the displacement-time graph for horizontal motion should be linear with a constant slope.
• Vertical Motion: The vertical displacement is influenced by gravity, meaning it will be uniformly accelerated motion. Therefore, the displacement-time graph for the vertical component should be a curve representing increasing displacement with time (quadratic relationship).

Graph Analysis:

• For the Vertical Component:

  • A curved line indicates increasing vertical displacement over time due to the acceleration from gravity (parabolic shape).

• For the Horizontal Component:

  • A straight line with a constant slope signifies uniform motion, which aligns with the assumption of no air resistance.

Correct Pair:

• Based on this understanding, the correct graph pair should show a curved graph for vertical displacement and a straight-line graph for horizontal displacement. From the provided options in the images:
  • The correct answer is C.

This pair shows a curved vertical displacement graph (due to gravitational acceleration) and a straight horizontal displacement graph (due to constant velocity).

Would you like further details on any part of this analysis?

Here are some related questions you might find interesting:

1. How is the equation for vertical displacement derived from uniformly accelerated motion?
2. What role does gravity play in horizontal projectile motion?
3. How does the absence of air resistance affect the displacement graphs?
4. How would the graphs change if air resistance were considered?
5. Can horizontal and vertical motions affect each other in projectile motion?

Tip: In projectile motion, the horizontal and vertical motions are independent of each other, with gravity only acting vertically.