Question

Prove that a projectile of an object is parabola

Answer 1

A projectile is an object upon which the only force is gravity. Gravity, being a downward force, causes a projectile to accelerate in the downward direction. The force of gravity could never alter the horizontal velocity of an object since perpendicular components of motion are independent of each other. A vertical force does not effect a horizontal motion. The result of a vertical force acting upon a horizontally moving object is to cause the object to deviate from its otherwise linear path.
OR

A parabolic path is the path followed by a projectile; that is, an object that is only acted on by gravity. The projectile has an initial velocity, either horizontal or upward at an angle. If it were to start out going straight up, it would go straight down, too, so that wouldn't be much of a parabola; it would be squished into a straight line. It would be the same way if it started out going straight down, or if we simply dropped it, so we'll really be looking at the parabolic paths followed by projectiles with some initial velocity.