Answer:
Parabola
Explanation:
The motion of a projectile consists of two independent motions:
- A uniform motion along the horizontal (x) direction, with constant velocity [tex]v_x[/tex]. In fact, there are no forces acting along this direction (if we neglect air resistance), so the acceleration is zero and the velocity is constant
- An uniformly accelerated motion along the vertical (y) direction, with constant acceleration [tex]g=9.8 m/s^2[/tex] downward (acceleration due to gravity). This acceleration is due to the force of gravity that pulls the projectile downward.
The composition of these two motions gives a parabolic trajectory. In fact, the equations of the motion along the two directions are:
[tex]x(t) = v_x t[/tex] (1)
[tex]y(t) = h + v_y t - \frac{1}{2}gt^2[/tex] (2)
Solving for t in eq.(1),
[tex]t=\frac{x}{v_x}[/tex]
and substituting into (2)
[tex]y(t) = h + \frac{v_y}{v_x}x - \frac{1}{2}g(\frac{x}{v_x})^2[/tex]
which is the equation of a parabola.
