Independent horizontal and vertical motions determine total speed

Steps:

• Horizontal velocity remains constant at 10 m/s since no horizontal acceleration.
• Vertical velocity just before impact: initial v_y = 0, so v_y = g t ≈ 9.8 m/s² × 3 s = 29.4 m/s downward.
• Total speed: magnitude of velocity vector, v = √(v_x² + v_y²) = √(10² + 29.4²) ≈ √(100 + 864) ≈ √964 ≈ 31 m/s.

Why C is correct:

• Speed is the Pythagorean combination of constant horizontal velocity and acquired vertical velocity from gravity, per v = √(v_x² + (gt)²).

Why the others are wrong:

• A: Equals initial horizontal speed only, neglects vertical component from gravity.
• B: Matches vertical speed alone (gt ≈ 29 m/s), ignores horizontal component.
• D: Overestimates by incorrectly adding components (10 + 29 ≈ 39) instead of using vector magnitude.

Final answer: C