Question

Show that a path followed by a projectile is parabola

Answer 1

For motion in horizontal direction , let displacement in horizontal is x.

The horizontal component of initial velocity u is ucosα , where α is the angle of projection.

If time taken is t , acceleration in x direction is =0, then

x=ucosαt

⇒t=x/ucosα

Now for y direction , vertical component of initial velocity = usinα

displacement in vertical direction = y

acceleration in vertical direction = -g

So equation

y=usinαt - 1/2gt²

substituting the value of t=(x/ucosα)

y=usinα(x/ucosα) - 1/2g(x/cosα)²

y=u²xtanα  -gx²sec²α

This equation is a quadratic equation in x , we know that a quadratic equation is  a parabolic curve , so this is a equation of a parabola.