1. The horizontal distance traveled by a projectile, neglecting air resistance, is given by the equation \( \text{range} = \frac{v^2 \sin(2\theta)}{g} \), where \(v\) is the initial velocity of the projectile, \( \theta \) is the launch angle, and \(g\) is the acceleration due to gravity.
2. The time of flight of a projectile can be calculated using the equation \( T = \frac{2v \sin(\theta)}{g} \), where \(T\) is the time of flight.
3. The maximum height reached by a projectile can be determined by the equation \( H = \frac{v^2 \sin^2(\theta)}{2g} \), where \(H\) is the maximum height.
4. The vertical displacement of the projectile at any time \( t \) can be calculated using the equation \( y = v \sin(\theta) t - \frac{gt^2}{2} \).
5. The horizontal displacement of the projectile at any time \( t \) can be determined by the equation \( x = v \cos(\theta) t \).
6. The projectile's velocity at any time \( t \) can be found by combining its horizontal and vertical components using the equations \( V_x = v \cos(\theta) \) and \( V_y = v \sin(\theta) - gt \).
6 equations of projectile motion
1 answer