Projectile motion components determine displacement graphs

Steps:

• Horizontal motion has uniform velocity, so displacement $s_h = vt$, linear with time.
• Vertical motion has uniform acceleration from rest, so displacement $s_v = \frac{1}{2}at^2$, quadratic (parabolic) with time.
• Total displacement magnitude combines both, but graphs specify components.
• Correct graph matches vertical parabolic shape.

Why D is correct:

• Vertical displacement follows $s = \frac{1}{2}gt^2$ (constant acceleration from rest), producing a parabolic curve.

Why the others are wrong:

• A: Linear graph suits horizontal uniform velocity, not vertical acceleration.
• B: Incorrect shape for vertical; likely linear, ignoring quadratic acceleration.
• C: Linear graph fits horizontal, not the accelerated vertical motion.

Final answer: D