Projectile motion is the movement of an object that is thrown into the air and allowed to move along a curved path under the influence of gravity alone.

Understanding Trajectory

The path followed by a projectile is called its trajectory. Because gravity pulls the object downward, the path is always a curve known as a parabola. Imagine throwing a basketball toward a hoop. The ball does not go in a straight line; it arches up and then falls back down. This curved path is the direct result of gravity constantly changing the object's vertical speed.

Time of Flight and Maximum Height

The time of flight is the total time the object stays in the air from the moment it is thrown until it hits the ground. This depends on how high you throw the object. The maximum height is the highest point the projectile reaches. At this specific peak, the object's vertical velocity becomes zero for a tiny fraction of a second before it begins to fall back down. To reach a higher peak, you must give the object a faster initial upward push.

Calculating Range

The range is the horizontal distance traveled by the projectile from the starting point to the landing point. If you throw a ball at a 45-degree angle, you will generally achieve the maximum range. Gravity pulls the object down, but its horizontal speed remains steady if we ignore air resistance. The range formula is: R = (v² * sin(2θ)) / g, where 'v' is the starting speed, 'θ' is the angle, and 'g' is the gravity of Earth.

Real-World Examples

• A kicked football soaring through the air to reach the goal.
• A water stream coming out of a garden hose.
• A javelin thrown by an athlete in a track and field event.
• A baseball hit by a batter traveling deep into the outfield.