Time of flight determined by vertical velocity

Steps:

• Maximum height h = (v_y^2)/(2g), where v_y is initial vertical velocity component; same h means same v_y for X and Y.
• Total time of flight T = 2 v_y / g for both, as vertical motion is identical.
• X has only vertical velocity, Y has horizontal component, but time depends solely on vertical.
• Both return to ground when vertical displacement is zero, taking time T.

Why C is correct:

• Time of flight formula T = 2 v_y / g shows it depends only on initial vertical velocity and g, which are the same for equal heights.

Why the others are wrong:

• A: At maximum height, vertical velocity is zero, but Y has horizontal velocity, so not at rest.
• B: Y requires higher total speed to achieve same v_y due to horizontal component.
• D: X travels zero horizontal distance; Y travels range, so different distances.

Final answer: C