Question

Prove that the path of a projectile is in parabolic shape

Answer 1

in projectile motion
1) horizontal velocity constant
2) virtical velocity varies
let a body projected with a velocity v and initai inclination of velocity with horizontal is @ .
Ux=vcos@ , Uy=vsin@
now
use kinematic equation ,
X=Ux.t+1/2a.t^2
but in horizontal a=0
so,
X=Ux.t
=vcos@t.
t=x/vcos@ ------------------(1)

for y -component
Y=Uy.t+1/2at^2
in vertical a=-g
hence,
[email protected]/2gt^2
use t=X/vcos@ here
Y=vsin@X/vcos@-1/2gX^2/v^2cos^2@

[email protected]^2/2v^2cos^2@

here we see trajectory of body like parabola equation .
hence projectile motion is in projectile shape.