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.

Question

Deborah Walter

Mathematics

24 June, 04:18

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.

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Norris · Answer 1

Answer: y = v₀tgθx - gx²/2v₀²cos²θ

a = v₀tgθ

b = - g/2v₀²cos²θ

Step-by-step 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