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Enter velocity, angle, and height to instantly calculate flight time, range, and view the trajectory graph with step-by-step calculations.
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This Projectile Motion Calculator quickly determines the time of flight, maximum height, horizontal range, and final velocity of a projectile launched with a given initial velocity, launch angle, and initial height. It also calculates the position and velocity at any specified time (t) during flight.
Our tool includes a graphical trajectory display and step-by-step calculations to help students and professionals clearly understand each stage of projectile motion.
In physics, projectile motion describes the motion of an object launched into the air that moves under the influence of gravity alone (assuming air resistance is negligible).
The path followed by the object is called its trajectory, the object itself is known as a projectile, and the motion is referred to as projectile motion.
Projectile motion can be resolved into two independent components:
Although these motions occur simultaneously, they are analyzed separately.
The combined effect of constant horizontal velocity and vertical acceleration produces a parabolic trajectory. The shape of the path depends on:
This projectile motion solver helps students, teachers, engineers, and researchers analyze motion quickly and accurately. It combines:
Common real-world applications include:
Vx = V cos(θ)
Vy = V sin(θ)
T = (2Vy) / g
R = (2VyVx) / g
or
R = (V² sin(2θ)) / g
H = (Vy²) / (2g)
Vx = V cos(θ)
Vy = V sin(θ)
T = (Vy + √(Vy² + 2gh)) / g
R = Vx × T
H = h + (Vy²) / (2g)
A ball is thrown with an initial velocity of 25 m/s at an angle of 40° from ground level. Assume g = 9.8 m/s² and no air resistance.
T = (2 × 16.08) / 9.8 = 3.28 s
H = (16.08²) / (2 × 9.8) = 13.19 m
R = 19.15 × 3.28 = 62.78 m
| Parameter | Symbol | Result | Unit |
|---|---|---|---|
| Time of Flight | T | 3.28 | s |
| Maximum Height | H | 13.19 | m |
| Horizontal Range | R | 62.78 | m |
When launch and landing heights are equal and air resistance is ignored, maximum range occurs at θ = 45°.
From the equation R = (V² sin(2θ)) / g, maximum range occurs when sin(2θ) = 1. This happens when 2θ = 90°, therefore θ = 45°.
No — in the ideal model without air resistance, mass does not affect range. According to Newton’s second law (F = ma), gravitational acceleration (g) is constant for all objects. Therefore, projectiles launched with the same velocity and angle follow identical trajectories regardless of mass.
If a projectile is launched from an elevated height, it remains in the air longer, increasing the total time of flight and typically increasing horizontal range.
Yes. Air resistance (drag) reduces maximum height, time of flight, and horizontal range. The trajectory is no longer perfectly parabolic when drag is considered.
Yes, as long as the projectile is moving under gravity alone and air resistance is negligible. The calculator is based on standard 2D kinematics equations.
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