Projectile Motions

Naturally after learning about the big 5 equations we will move onto projectile motions. A simple type of projectile question would be if a fired a projectile at a certain initial velocity at a certain angle of elevation, how far would it travel. To solve these types of questions, first we must split it into two parts, the x and y components. The y component is used to figure out how long the projectile is in the air while the x component is to figure out the speed at which it travels horizontally. Naturally we will be assuming that this is occurring on earth and that there is no air resistance.
Y component
The initial vertical speed of the projectile can be defined as v sin(degrees). Since we are on earth, we can assume that the acceleration is -9.8 m/s^2 which is the gravity pulling it down and that eventually it will fall to a velocity of 0 m/s. At that point it will fall down using the same amount of time taken to get to that point. Thus the time the projectile is in the air can be expressed as t = 2(v2-v1/a) which will allow us find the time it is in the air.
X component
Unlike the y component, if we assume that there is no air resistance, there won't be any force acting against the projectile. Thus the horizontal speed of the projectile can be simply expressed as v cos(degrees).

With these two pieces of information, the distance that the projectile travels can simply be expressed as d = vt