Question

Prove that the path followed by the projectile under an angular projection is a parabola.plzzsszszs guys ans fasssst

Answer 1

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Answer 2

According to the given data apply the equation of motion in 2D motion, and we get the angle of projection be $\alpha$

Thereby $u y = u cos \alpha$

And $u x = u sin \alpha$

And x = 0 and y = -g

From equation of motion, we have

$t=\frac { x }{ ucos\alpha }$

$y = u sin \alpha - \frac {1} {2} g t^2$

$\Rightarrow$ from both equation, we can get the equation of motion as

$y=usin\alpha \times \frac { x }{ ucos\alpha } -\frac { 1 }{ 2 } g(\frac { x }{ ucos\alpha } )^{ 2 }$

And thereby

$y=tan\alpha x-\frac { gx^{ 2 } }{ 2u^{ 2 }cos^{ 2 }\alpha }$

Which implies the equation of $y = a x^2 + bx + c$ which is an symbolic equation of parabola thus the projectile motion follows a parabolic path.