Relative velocity: it depends who's asking
Walk forward at 1 m/s along a train that moves at 15 m/s past the platform, and the platform sees you go at 16 m/s. Velocities measured in different frames of reference differ, and relative velocity is the rule for converting between them: your velocity relative to the ground is your velocity relative to the train, plus the train's velocity relative to the ground.
A's velocity relative to C equals A's relative to B plus B's relative to C. The inner subscripts match and cancel — a handy bookkeeping check. These are vector additions, so directions matter.
A full projectile problem
Let us fire a projectile at v_0 = 20\text{ m/s} and \theta = 30° on Earth (g = 9.8\text{ m/s}^2), landing at launch height, and find its range. First the components: v_{0x} = 20\cos30° \approx 17.3\text{ m/s} and v_{0y} = 20\sin30° = 10\text{ m/s}. The time of flight is T = 2v_{0y}/g = 20/9.8 \approx 2.04\text{ s}, and the range is R = v_{0x}\,T \approx 17.3 \times 2.04 \approx 35.3\text{ m} — matching R = v_0^2\sin2\theta/g. Use the widget below to check that a launch of 60° gives the same range, and that 45° beats both.
A strategy that always works
Where this leads next
You can now describe motion completely — position, velocity, acceleration, in one and two dimensions. But we never asked why the car accelerates or why the ball follows a parabola. Every acceleration you have met is caused by a force, and the bridge from 'describing' to 'explaining' is Newton's second law, the start of dynamics. From there, energy and momentum offer even more powerful shortcuts, and the same graph-and-limit thinking you used here becomes the gateway to calculus. Kinematics is the vocabulary; the rest of physics is the conversation.