What is the analytical equation for determining the trajectory of a projectile?

The analytical equation for determining the trajectory of a projectile is the projectile motion equation, which is given by:

y xtan - (gx2) / (2v2cos2)

where:

• y is the vertical position of the projectile
• x is the horizontal position of the projectile
• is the launch angle
• g is the acceleration due to gravity (approximately 9.81 m/s2)
• v is the initial velocity of the projectile