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Range of ProjectileMotion in two dimensions - calculate the range of a projectile like a bullet, ball ...
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The time for a projectile, or a ball or a stone or something similar - thrown out with an angle Θ to the horizontal plane - to reach the maximum heightcan be calculated as
th = vi sin(Θ) / g (1)
where
th = time to reach maximum height (s)
vi = initial velocity of the projectile (m/s, ft/s)
Θ = the initial angle of the velocity vector to the horizontal plane (degrees)
g = acceleration of gravity (9.81 m/s2, 32.174 ft/s2)
The total flight time can be expressed as
ts = 2 th
= 2 vi sin(Θ) / g (2)
where
ts = time for the total flight (s)
The maximum elevation - h - of the flight can be calculated as
h = 1/2 g th2 (3)
where
h = flight maximum elevation (m, ft)
The horizontal distance of the flight can be expressed as
s = vi2 sin(2 Θ) / g (4)
where
s = flight distance (m, ft)
Example - Throwing a BallA ball is thrown with initial velocity 25 m/s in angle 30 degrees to the horizontal plane. The time for the ball to reach maximum level is
th = (25 m/s) sin(30 degrees) / (9.81 m/s2)
= 1.27 s
The maximum elevation of the ball can be calculated as
h = 1/2 (9.81 m/s2) (1.27 s)2
= 7.91 m
The horizontal distance traveled by the ball can be calculated as
s = (25 m/s)2 sin(2 30 degrees) / (9.81 m/s2)
= 55.2 m
Projectile Flight CalculatorThe calculator below can be used to estimate the time of flight, time to reach maximum elevation, maximum elevation and flight distance for aprojectile like a bullet or a ball or something similar. Note that friction forces due to air resistance is neglected.
25 vi - initial velocity (m/s)
30 Θ - initial angle to the horizontal plane (degrees)
Calculate!
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Related Topics
Mechanics - Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objectsDynamics - Dynamics Motion - velocity and acceleration
Related Documents
Formulas of Motion - Linear and Circular - Linear and angular (rotation) acceleration, velocity, speed and distanceAcceleration of Gravity and Newton's Second Law - Acceleration of gravity and Newton's Second Law - SI and Imperial units
Tag Search
en: range projectile movement two dimensions bullet balles: rango de movimiento de proyectil dos dimensiones bulletde: Bereich Projektilbewegung zwei Dimensionen Kugel Ball
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