A projectile is any object that is given an initial velocity, then follows a path determined by gravity. Motion is the change in position of an object. Projectile motion is the combination of both terms, that being said, it is the motion of an object thrown at angle where only one force is acting upon it, the force of gravity.
In this experiment, data is acquired from the projectile that is launched in several angles using different equations. Additionally, one gets to know how the different tools and equations involved are used while at the same time, obtaining a firmer grip on how projectile motion works.

Projectile Motion is the free fall motion of any body in a horizontal path with constant velocity.
The students are to obtain the Vertical Distance which is the distance between the table and the ball before launch and Horizontal Distance which is the distance travelled by the ball horizontally. With the following equations, one can now compute for the time (1), initial velocity (2), and acceleration due to gravity (3) of projectile fired horizontally.

(1) t = √(2Δy/g)
(2) Vo = Δx/(t cos⁡θ )
(3) g = (2(Δx tan⁡〖θ+ Δy )〗)/t^2

When the projectile is fired at different angles, the equations for the time (4), initial velocity (2), and acceleration due to gravity (3) will now be different.

(4) t = Δx/(v cos⁡θ )
(5) Vo = √2gΔy/sin⁡θ
(6) g = (2(Δx tan⁡〖θ - Δy )〗)/t^2

The t represents time, Vo represents initial velocity, g stands for acceleration due to gravity, ∆x means the horizontal distance and ∆y means vertical distance.
In part 2 of the experiment, the ball is once again launched from the launcher and both distances, Vertical and Horizontal, are measured. Use equation (7) to get the mean value of the distances.

(7) x = (x_1+ x_2+ x_3+⋯+ x_n)/n

To get the time of flight of the ball, use equation (1) and use equation (2) to calculate the initial velocity of the ball.

(8) ∆x =V_O cos⁡〖θ t〗
(9) % Difference = |∆x_1- ∆x_2 |/(((∆x_1+ ∆x_2)/2)) x 100
(10) t= √((2(∆y - ∆x_(1 tan⁡θ ))/g)

If the projectile is fired at a different angle, use equation (10) to get the time of flight of the ball, equation (8) to calculate the computed displacement, and equation (9) to compute for the % Difference.

Projectile Motion
Group No. 6; 1CSB
M, Jeorjette J. T.
M, Juan C. T.
P, Carl V. M.
P, Gianne J. T.
R, John C. S.

L, Lyza M. G.

Projectile Motion (n.d.). Retrieved from http://formulas.tutorvista.com/physics/projectile-motion-formula.html