Resolving velocity into horizontal and vertical components

Steps:

• Identify the total velocity vector with magnitude v at angle θ to the horizontal.
• Decompose into horizontal (x) and vertical (y) components using trigonometry.
• Horizontal component is v times the cosine of θ, as cos θ = adjacent/hypotenuse.
• Magnitude of horizontal component is v cos θ.

Why B is correct:

• The horizontal component of a velocity vector is defined as v cos θ, where θ is the angle to the horizontal axis.

Why the others are wrong:

• A and C: v sin θ represents the vertical component, not horizontal.
• D: (v_y)^2 is the square of the vertical velocity component, unrelated to horizontal magnitude.

Final answer: B