Projectile Motion

Projectile motion is the curved path of an object that is thrown and then moves only under gravity, like a cricket ball, a javelin or water from a hose. Its horizontal speed stays constant while gravity changes its vertical speed, which bends the path into a parabola.

For a projectile launched and landing at the same height, range R = u² sin 2θ / g, where u is the launch speed, θ the launch angle and g the acceleration due to gravity. The maximum range is u²/g, at θ = 45°.

Maximum height H = u² sin²θ / 2g. It depends only on the vertical part of the launch velocity, u sin θ.

Time of flight T = 2u sin θ / g when it lands at the same height it was launched from. The time to reach the top is half of this, u sin θ / g.

Range depends on sin 2θ, which is largest (equal to 1) when 2θ = 90°, so θ = 45°. That angle balances time in the air against horizontal speed. When launched from a height, like a cliff, or with air resistance, the best angle is a little less than 45°.

Yes, if air resistance is ignored. No horizontal force acts on the projectile, so its horizontal velocity u cos θ stays the same throughout the flight. Only the vertical velocity changes, by g every second.