Horizontal range in projectile motion Steps:

• Horizontal velocity is constant: V_x = V cos θ (no horizontal acceleration).
• Time of flight is T, so horizontal distance R = V_x × T.
• Vertical motion determines T but doesn't affect horizontal displacement.
• Thus, R = (V cos θ) T, matching option D.

Why D is correct:

• It follows the formula for range under constant horizontal velocity, R = V_x T.

Why the others are wrong:

• A: Omits time T, underestimating range unless T=1 (not general).
• B: Uses vertical velocity V sin θ and subtracts vertical displacement term, irrelevant for horizontal range.
• C: Applies vertical acceleration term to horizontal motion, which has no such effect.

Final answer: D