Horizontal displacement of projectile

Let’s say we throw the body at an angle to the horizon with some initial velocity. Then the horizontal displacement, or range, of the body depends on the initial speed, the angle of the throw and the acceleration of free fall.

Conditions:

1. The acceleration due to gravity is constant throughout the movement of the projectile.

2. The elevation of the initial and final points of the projectile are the same.

Links:

1. Physics LibreTexts. Projectile Motion, Range (3.3.15).

horizontal_displacement

Horizontal displacement, or range, of the projectile. See euclidean_distance.

Symbol:

d

Latex:

\(d\)

Dimension:

length

initial_speed

Initial speed of the projectile.

Symbol:

v_0

Latex:

\(v_{0}\)

Dimension:

velocity

angle

angle between the initial velocity and the horizon.

Symbol:

phi

Latex:

\(\varphi\)

Dimension:

angle

law

d = v_0^2 * sin(2 * phi) / g

Latex:

\[d = \frac{v_{0}^{2} \sin{\left(2 \varphi \right)}}{g}\]