Question

Prove that the trajectory of a projectile is parabolic, having the form y=ax+bx². To obtain this expression, solve the equation x=v₀xt for t and substitute it into the expression for y=v₀yt–(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.

The trajectory of a projectile is described by the equation:
a) y = ax
b) y = bx²
c) y = ax + bx²
d) y = ax - bx²

Answer 1

The trajectory of a projectile is proven to be parabolic by solving for time in the horizontal motion equation and substituting it into the vertical motion equation, yielding an equation of the form y = ax + bx².

Step-by-step explanation:

To derive the parabolic trajectory of a projectile, we first solve the horizontal motion equation for time (t), which is expressed as t = x / v0x. We then substitute this expression for t into the vertical motion equation, y = v0yt - (1/2)gt2. This substitution yields the equation y = (v0y / v0x)x - (g / 2v0x2)x2. Upon simplification, we obtain an equation of the form y = ax + bx2, where a = v0y / v0x and b = -g / 2v0x2, thus showing that the trajectory is a parabola.