write the expression for horizontal range and maximum height of a projectile
Write the expression for horizontal range and maximum height of a projectile
Expression for Horizontal Range:
The horizontal range of a projectile is the horizontal distance traveled by the projectile before it hits the ground. The formula to calculate the horizontal range, ( R ), of a projectile when launched at an angle ( \theta ) with an initial velocity ( v_0 ) is given by:
R = \frac{v_0^2 \times \sin(2\theta)}{g}
where:
- ( R ) = horizontal range
- ( v_0 ) = initial velocity of the projectile
- ( \theta ) = launch angle
- ( g ) = acceleration due to gravity (typically 9.81 m/s² on Earth)
Expression for Maximum Height:
The maximum height reached by a projectile is an essential parameter in projectile motion. The formula to calculate the maximum height, ( H ), of a projectile launched at an angle ( \theta ) with an initial velocity ( v_0 ) is given by:
H = \frac{v_0^2 \times \sin^2(\theta)}{2g}
where:
- ( H ) = maximum height
- ( v_0 ) = initial velocity of the projectile
- ( \theta ) = launch angle
- ( g ) = acceleration due to gravity
Understanding these expressions is crucial in analyzing the motion of projectiles in physics.