Final answer:
The trajectory of a projectile is shown to be parabolic by isolating time (t) from the horizontal motion equation and substituting it into the vertical motion equation. This substitution yields a quadratic equation in terms of x, confirming the parabolic nature of the projectile's path.
Step-by-step explanation:
To prove that the trajectory of a projectile is parabolic, we begin by solving the equation x = Voxt to find the value of t, which represents time. The initial velocity in the x-direction is denoted by Vox.
Once t is isolated in the equation, we substitute it into the equation for the y position: y = Voyt - (1/2)gt2, where Voy is the initial velocity in the y-direction, and g is the acceleration due to gravity.
Through substitution, we eliminate t and obtain a new equation in terms of x, y = ax + bx2, where a and b are constants. The constants a and b can be expressed as a = Voy/Vox and b = -g/2Vox2. This equation is a quadratic equation, representing a parabolic path of the projectile.