The trajectory of a projectile is y=ax−bx², where a,b0. Which statements are correct?

Question

The trajectory of a projectile is y=ax−bx², where a,b>0. Which statements are correct?

G1 Physics · Accepted Answer

Compare y=ax−bx² with the standard projectile equation y=x tanθ − gx²/(2u²cos²θ). Thus a=tanθ, b=g/(2u²cos²θ). The second root of y=0 gives the range: R=a/b. The vertex of the parabola occurs at x=a/(2b), and its height is H=a²/(4b). Also cos²θ = 1/(1+tan²θ) = 1/(1+a²). Therefore b = g(1+a²)/(2u²), so u² = g(1+a²)/(2b). Hence all four statements are correct.