Question: What is the trajectory of a projectile that is accelerated only due to the influence of gravity? Air resistance is neglected.

Fundamental point: The initial velocity is not colinear with the force!

Answer: Solve the kinematic equations of motion!

x(t)=v_x(0)t; y(t)=v_y(0)t -½gt²

Solve for t in the first equation, t=x(t)/v_x(0), and substitute in the second equation to give:

y(t)=v_y(0)x(t)/v_x(0) -½g[x(t)/v_x(0)]²= Ax+Bx² Parabolic trajectory!

Examples: thrown ball, bowling ball with sidespin, billiards masse shot.