A ball is projected at an angle. How should I find its velocity at a later time without mixing up speed and direction?
Think of the launch velocity as two teammates.
Think of the launch velocity as two teammates. The horizontal one keeps its value: v_x = u cos(theta). The vertical one changes under gravity: v_y = u sin(theta) - gt. Keep their signs. The velocity vector is v_x i + v_y j; only after that find speed as sqrt(v_x^2 + v_y^2) and direction from tan(phi) = v_y/v_x. This order prevents the common mistake of subtracting gt from the total speed.
Key point
Update only v_y under gravity; recombine components at the end.
Common mistake
using v = u - gt for the full two-dimensional velocity.
Memory tip
split, evolve, recombine.
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