Projectile Motion: Thrown Vertically and at an Angle
One acceleration, two independent motions: how gravity shapes every thrown ball, arrow and jet of water.
Big idea: Once a body leaves your hand and only gravity acts on it, its acceleration is fixed: g pointing straight down, with magnitude g = 9.8 m/s2 (we often round to 10 m/s2). The clever part is that the horizontal and vertical motions are completely independent. Vertically the body is in free fall; horizontally it just coasts at constant speed. Split every problem into these two directions and the mathematics becomes the uniformly-accelerated formulas you already met in topic 1.
By the end you will be able to:
- write the equations for a body thrown vertically up or down,
- find maximum height, time of rise and time of flight,
- resolve a launch velocity into vx and vy with sine and cosine,
- derive and use the range, height and time-of-flight formulas for a body thrown at an angle,
- explain why 45° gives the greatest range and why the path is a parabola.