Velocity Components and Angle Steps:

• The velocity V forms a right triangle with horizontal component V_x and vertical component V_y.
• Magnitude V is the hypotenuse: V = √(V_x² + V_y²) by Pythagorean theorem.
• Angle θ to horizontal satisfies tanθ = opposite/adjacent = V_y / V_x.
• Thus, θ = tan⁻¹(V_y / V_x), matching option A.

Why A is correct:

• It uses Pythagorean theorem for vector magnitude and tangent definition for angle from horizontal.

Why the others are wrong:

• B: Magnitude correct, but tan⁻¹(V_x / V_y) gives angle to vertical, not horizontal.
• C: √(V_x² - V_y²) subtracts components, invalid for magnitude.
• D: Subtraction for magnitude is wrong, and tan⁻¹(V_x / V_y) is angle to vertical.

Final answer: A