The formula for the maximum height of a projectile, assuming it is launched vertically or at an angle, can be derived from the equations of motion under constant acceleration due to gravity. The specific formula can vary depending on the initial conditions of the projectile's launch.
- For projectiles launched vertically:
If a projectile is launched straight up with an initial velocity \( v_0 \), the maximum height \( H \) reached can be calculated using the formula:
\[ H = \frac{v_0^2}{2g} \]
where:
- \( H \) = maximum height
- \( v_0 \) = initial velocity (m/s)
- \( g \) = acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \) on Earth)
- For projectiles launched at an angle:
If the projectile is launched at an angle \( \theta \) with an initial velocity \( v_0 \), the vertical component of the initial velocity is \( v_{0y} = v_0 \sin(\theta) \). The maximum height \( H \) is then calculated using:
\[ H = \frac{(v_0 \sin(\theta))^2}{2g} \]
In both cases, it is assumed that air resistance is negligible and the only force acting on the projectile after launch is gravity.
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