Question

Show that the trajectory of an object thrown at certain angle with the horizontal is a prabola

Answer 1

Answer:

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An object is thrown at an angle θ from the horizontal.

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Equation of trajectory

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We will divide the projectile motion into 2 different linear motion in x and y axes.

Time = T

Velocity in x axis = v cos(θ)

Velocity in y axis = v sin(θ)

Distance in x Axis =x= [v cos(θ)] × T .....(i)

Distance in y Axis

y = v sin(θ) × T - ½gT² ...........(ii)

Putting value of T in eq.(ii)

y = x × v sin(θ)/ v cos(θ) - ½g{x/vcos(θ)}²

y = x tan(θ) - gx²/2u²cos²(θ).

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The derived equation is some to a parabolic equation

y = ax - bx².

So the trajectory of a projectile is a Parabola.

Answer 2

Answer:

y= Ax-Bx^2 represents the equation of parabola.