Projectile Motion - Initial Velocity from Range
Projectile Motion - Initial Velocity from Range
\[v_0 = \sqrt{\frac{R g}{\sin(2\theta)}}\]
Variables
v0 = initial velocity (m/s)
R = horizontal range (m)
g = gravitational acceleration (m/s²)
theta = launch angle (rad)
Description
What is this formula?
This equation calculates the required initial velocity of a projectile to reach a specified horizontal range at a given launch angle.
When to use it
Use this formula when the target distance and launch angle are known and ideal projectile motion is assumed.
Example
If a projectile must travel 80 m with a launch angle of 45°:
v0 = ?((80 × 9.81) / sin(90°)) = 28.01 m/s
Applications
Ballistics, sports trajectory design, engineering simulations, targeting systems, and educational physics problems.
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