Projectile Motion Displacement Components

Steps:

• In projectile motion with negligible air resistance, horizontal velocity is constant, so horizontal displacement increases linearly with time.
• Vertical velocity changes due to constant gravitational acceleration, so vertical displacement follows a parabolic curve with time.
• Graph q shows linear increase, matching horizontal displacement.
• Graph p shows parabolic variation, matching vertical displacement.

Why B is correct:

• Horizontal displacement is $s_x = v_x t$ (linear), and vertical is $s_y = v_{y0} t - \frac{1}{2} g t^2$ (parabolic), aligning q with horizontal and p with vertical.

Why the others are wrong:

• A: Assigns q (linear) to vertical, but vertical displacement is parabolic, not linear.
• C: Assigns r to horizontal, but r does not show linear increase.
• D: Assigns r to horizontal and q to vertical, mismatching both linear and parabolic behaviors.

Final answer: B