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# Public Formula Library

### FLIGHT PATH

Just for viewing purposes. You can store and calculate this formula only inside the application.

### Formula name

FLIGHT PATH

### Description

slanting throw trajectory

### Syntax

/* The horizontal and vertical position of a ball thrown with a velocity v0 and an inclination angle φ to the horizontal line are time dependent

( named x(t) and y(t) respectively). */

x(t) = v0 * COS(φ) * t

/* Because of gravity the vertical velocity varies with the time : v(t) = v0 * SIN(φ) - [g] * t .

Because the acceleration [g] is constant, the distance covered during the time t is (( v0 + v(t) )/2 *t so that */

y(t) = v0 * SIN( φ) * t - [g] / 2 * t^2

/* The vertical position y can also be calculated in function of the horizontal position x by replacing the variable t in the second equation

by x /( v0 * COS(φ)). */

( named x(t) and y(t) respectively). */

x(t) = v0 * COS(φ) * t

/* Because of gravity the vertical velocity varies with the time : v(t) = v0 * SIN(φ) - [g] * t .

Because the acceleration [g] is constant, the distance covered during the time t is (( v0 + v(t) )/2 *t so that */

y(t) = v0 * SIN( φ) * t - [g] / 2 * t^2

/* The vertical position y can also be calculated in function of the horizontal position x by replacing the variable t in the second equation

by x /( v0 * COS(φ)). */

### Notes

SIN(φ) / COS(φ) = TAN(φ)

### Category / Subcategory

Physics / Kinematics

### Creator

pbrodmann@brodmann.biz

### Account

Premium

### Tags

acceleration velocity horizontal postition

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