Projectile motion: Shape of trajectory under uniform gravity Statement to evaluate: "The path (trajectory) of an ideal projectile is a parabola." Choose the correct truth value.

ConceptWith constant gravitational acceleration and no air resistance, horizontal motion has constant velocity while vertical motion has constant acceleration.

Derivation sketchLet initial speed be u and angle θ. Then: x = (u cosθ) t y = (u sinθ) t − (1/2) g t^2 Eliminate t = x/(u cosθ) to get y = x tanθ − (g x^2)/(2 u^2 cos^2θ) which is a quadratic in x — i.e., a parabola.

Final AnswerTrue