To calculate the time and distance of a projectile motion, you need to consider the initial velocity, launch angle, and the effects of gravity. Here's a step-by-step guide:
Resolve the initial velocity: Break down the initial velocity into its horizontal (Vx) and vertical (Vy) components. If the initial velocity is represented as V with an angle θ measured from the horizontal, then Vx = V * cos(θ) and Vy = V * sin(θ).
Calculate the time of flight: The total time of flight (T) is the duration of the projectile's motion from launch to landing. In the absence of air resistance, the time of flight is solely determined by the vertical motion and can be calculated using the equation: T = 2 * Vy / g, where g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth).
Determine the maximum height: The maximum height (H) reached by the projectile can be found using the equation: H = (Vy^2) / (2 * g).
Calculate the horizontal distance: The horizontal distance (R) covered by the projectile can be determined by multiplying the horizontal component of velocity (Vx) by the time of flight (T): R = Vx * T.
Note: These calculations assume idealized conditions of no air resistance and a uniform gravitational field. In reality, factors such as air resistance and variations in gravitational acceleration may slightly affect the projectile's motion.
By applying these formulas, you can determine the time of flight and distance traveled for a projectile in motion.