how parabolic projectile motion works?
Understand parabolic projectile motion in easy way.
Projectile motion describes the two-dimensional movement of an object that is launched with an initial velocity and then allowed to move under the influence of gravity alone. The horizontal and vertical motions are independent: horizontal motion has constant velocity (if we neglect air drag), while vertical motion experiences constant acceleration due to gravity.
In this simulation you can tune the launch speed v₀, the shooting angle θ, the initial height h₀, and even add linear drag or wind acceleration. The draggable ball lets you reposition the launch instantly, making it easier to investigate "what-if" scenarios.
- Horizontal position: x(t) = v₀ cos(θ) · t
- Vertical position: y(t) = h₀ + v₀ sin(θ) · t - ½ g t²
- Time of flight (until y=0): t_f = (v₀ sin(θ) + √(v₀² sin²(θ) + 2 g h₀)) / g
- Range: R = v₀ cos(θ) · t_f
Ignoring drag, the total mechanical energy E = K + U remains constant. At launch the kinetic energy is ½ m v₀² and the potential energy is m g h₀. As the projectile rises, kinetic energy is converted into potential energy until it reaches the apex.
- A 45° launch maximizes range only when h₀ = 0 and there is no drag.
- Higher launch heights increase the time of flight and therefore the horizontal range.
- Wind acceleration acts horizontally and can either stretch or shorten the range depending on its direction.
- Drag forces depend on velocity; faster projectiles experience a stronger decelerating effect.