Show that the path of projectile projected at an angle of THITA from horrizontal is parabolic in shape?

1 Answer
Feb 1, 2018

If the projectile is projected with a velocity u at an angle theta w.r.t horizontal,then horizontal component of its velocity is u cos theta due to which it moves forward,and vertical component of velocity is u sin theta due to which first it goes up then comes down due to gravity.

So,if in time t it goes X distance horizontally ,we can say,

(X = u cos theta*t)

Or, t=X/(u cos theta) ...1

And,if vertically it goes by distance Y then,

Y=u sin theta×t - 1/2 g t^2

Now putting the value of t in the above equation we get,

Y= X tan theta - 1/2 g X^2/(u^2 cos ^2 theta)

This can be compared with y=ax+bx^2 ,which is an equation of parabola