Projectile Motion - Horizontal Range
Projectile Motion - Horizontal Range
\[R = \frac{v_0^2 \sin(2\theta)}{g}\]
Variables
R = horizontal range (m)
v0 = initial velocity (m/s)
theta = launch angle (rad)
g = gravitational acceleration (m/s²)
Description
What is this formula?
This equation calculates the maximum horizontal distance traveled by a projectile launched with an initial velocity at a given angle above the horizontal.
When to use it
Use this formula when analyzing ideal projectile motion without air resistance and when the launch and landing heights are equal.
Example
If a projectile is launched at 25 m/s with an angle of 45°:
R = (25² × sin(90°)) / 9.81 = 63.71 m
Applications
Ballistics, sports physics, engineering simulations, motion analysis, and educational physics problems.
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