In more detail
The motion splits into two independent parts: horizontal velocity stays constant at v × cos θ, while vertical velocity starts at v × sin θ and falls by g every second, so the path is a parabola. On level ground the range is v² × sin(2θ) / g, the maximum height v² × sin²θ / (2g) and the time of flight 2v × sin θ / g. The range is greatest at 45°, and complementary angles such as 30° and 60° land at the same distance, the steeper one flying higher and longer.
Why it matters
It describes thrown balls, water jets and jumps well at low speeds. Air resistance shortens real trajectories and lowers the best launch angle below 45°, and launching from above the landing height lowers it too, which is why shot-putters release at a flatter angle. Keep units consistent: g is 9.81 m/s² or 32.2 ft/s².
Example
v = 20 m/s, g = 9.80665 m/s²
45°: range 40.79 m, max height 10.20 m, flight 2.88 s
30°: range 35.32 m, max height 5.10 m, flight 2.04 s
60°: range 35.32 m, max height 15.30 m, flight 3.53 s