Question

Prove that the trajectory of a projectile is parabolic, having the form y = ax + bx2. To obtain this expression, solve the equation x = v0xt for t and substitute it into the expression for y = v0yt − 1 2 gt2. (These equations describe the x and y positions of a projectile that starts at the origin.) You should obtain an equation of the form y = ax + bx2 where a and b are constants.

Answer 1

Answer: y = v₀tgθx - gx²/2v₀²cos²θ

a = v₀tgθ

b = -g/2v₀²cos²θ

Explanation:

x = v₀ₓt

y = v₀y.t - g.t²/2

x = v₀.cosθt → t = x/v₀.cosθ

y = v₀y.t - g.t²/2

v₀y = v₀.senθ

y = v₀senθ.x/v₀cosθ - g/2.(x/v₀cosθ)²

y = v₀.tgθ.x - gx²/2v₀²cos²θ

a = v₀tgθ → constant because v₀ and θ do not change

b = - g/2v₀²cos²θ → constant because v₀, g and θ do not change