Prove that the trajectory of a projectile is parabolic, having the form y = ax + bx2 . To obtain this expression, solve the equation x = v0x t for t and substitute it into the expression for y = v0y t – (1 / 2)gt2 (These equations describe the x and y positions of a projectile that starts at the origin.) You should obtain an equation of the form y = ax + bx2 where a and b are constants.
Step 1 of 5:
A projectile is a body that is thrown at air moves with certain initial velocity and travels under the action of velocity. The velocity of the projectile is either increasing or decreasing based on the location of the projectile. Finally, the projectile hits the ground and the velocity becomes zero. The path followed by the projectile is always a part of a parabola. Our aim is to prove that the trajectory of the projectile is a parabola.
Step 2 of 5:
The horizontal velocity of the projectile is denoted as which is constant over the period of time. The horizontal distance traveled by the projectile over the time t is given by
Since the projectile start from rest, , therefore the above equation becomes
Step 3 of 5:
At a particular instant of time , the projectile may reach vertical distance and velocity in the vertical direction is and this varies under the action of gravity.
The vertical distance traveled by the projectile