Range Projectile

Reference data and engineering information about range projectile for dynamics applications.

rangeprojectile

Overview

Engineering reference data for Range Projectile in dynamics.

$F = ma$

Force = mass × acceleration.

$E_k = \frac{1}{2}mv^2$

Energy of motion.

$p = mv$

Mass × velocity.

$W = Fd\cos\theta$

Force × displacement × cos(angle).

A ball is thrown with an initial velocity of 25 m/s at an angle of 30 degrees to the horizontal plane.

The time to reach maximum height is:

$t_h = \frac{v_i \sin(\Theta)}{a_g} = \frac{(25 \text{ m/s}) \cdot \sin(30^\circ)}{9.81 \text{ m/s}^2} = 1.27 \text{ s}$

The maximum elevation of the flight is:

$h = \frac{1}{2} a_g t_h^2 = \frac{1}{2} (9.81 \text{ m/s}^2)(1.27 \text{ s})^2 = 7.91 \text{ m}$

The horizontal distance traveled is:

$s = \frac{v_i^2 \sin(2\Theta)}{a_g} = \frac{(25 \text{ m/s})^2 \cdot \sin(2 \times 30^\circ)}{9.81 \text{ m/s}^2} = 55.2 \text{ m}$

Air resistance neglected: All calculations assume a vacuum with no air friction. In reality, drag forces significantly reduce both range and maximum height, especially at higher velocities.
Optimal angle: For maximum range on level ground (neglecting air resistance), the optimal launch angle is $45^\circ$ , since $\sin(2\Theta)$ reaches its maximum value of 1.
Symmetry: In the idealized case, the projectile's trajectory is symmetric about its highest point, meaning the time to ascend equals the time to descend.