write the expression for horizontal range and maximum height of projectile
Write the expression for horizontal range and maximum height of projectile
Horizontal Range Formula:
The horizontal range of a projectile is the horizontal distance traveled by the projectile before hitting the ground. The formula to calculate the horizontal range of a projectile launched at an angle θ with an initial velocity ( v_{0} ) is given by:
[ R = \frac{v_{0}^{2} \times \sin(2\theta)}{g} ]
where:
- ( R ) is the horizontal range,
- ( v_{0} ) is the initial velocity of the projectile,
- ( \theta ) is the angle of projection,
- ( g ) is the acceleration due to gravity (approximately 9.81 m/s²).
Maximum Height Formula:
The maximum height of a projectile is the highest vertical position reached by the projectile during its flight. The formula to calculate the maximum height of a projectile launched at an angle θ with an initial velocity ( v_{0} ) is given by:
[ H = \frac{v_{0}^{2} \times \sin^2(\theta)}{2g} ]
where:
- ( H ) is the maximum height reached by the projectile,
- ( v_{0} ) is the initial velocity of the projectile,
- ( \theta ) is the angle of projection,
- ( g ) is the acceleration due to gravity.
These formulas are essential in projectile motion problems to determine the horizontal range and maximum height achieved by the projectile.