find the expression for the time of flight maximum height and horizontal range of a projectile
Find the expression for the time of flight, maximum height, and horizontal range of a projectile
Time of Flight:
The time of flight of a projectile can be calculated using the formula:
$$ T = \frac{2 \cdot V_0 \cdot sin(\theta)}{g} $$
where:
( T ) = time of flight,
( V_0 ) = initial velocity of the projectile,
( \theta ) = angle of projection,
( g ) = acceleration due to gravity.
Maximum Height:
The maximum height reached by a projectile can be calculated using the formula:
H = \frac{V_0^2 \cdot sin^2(\theta)}{2g}
where:
( H ) = maximum height.
Horizontal Range:
The horizontal range of a projectile can be calculated using the formula:
R = \frac{V_0^2 \cdot sin(2\theta)}{g}
where:
( R ) = horizontal range.
These formulas are derived by analyzing the motion of a projectile under the influence of gravity. By plugging in the values of the initial velocity and angle of projection, you can calculate the time of flight, maximum height, and horizontal range of a projectile. These expressions are essential in understanding the motion of projectiles and can be used in various physics problems related to projectile motion.