Final answer:
The trajectory of a projectile is derived by substituting the solved equation for time, t, from horizontal motion x = Vot, into the vertical motion equation y = Voyt - (1/2)gt², ultimately obtaining a parabolic equation of the form y = ax + bx².
Step-by-step explanation:
The question pertains to the trajectory of a projectile being parabolic in nature. The equation of the trajectory can be expressed as y = ax + bx², demonstrating the parabolic path followed by a projectile. This is derived by solving the equation x = Vot for t and substituting it into the expression for y = Voyt - (1/2)gt², where Vox and Voy are the initial velocities in the x and y directions, respectively, and g is the acceleration due to gravity. Obtaining the equation in the form y = ax + bx² involves algebraic manipulation and represents the path of the projectile when launched from the origin, with a and b as constants determined by the initial conditions of projectile motion.
Moreover, the topic briefly mentions a parabola passing through the origin with a focus at (0, -1), suggesting the student's confusion with concepts related to optics involving lenses and ellipses. However, this information does not directly contribute to deriving the trajectory equation of a projectile, which is our main focus.