welcome that electron line and our next segment in physics is two-dimensional motion or motion in two dimensions and in order to understand a little bit better let's take a look at our example here we have two objects let's call them balls one that simply dropped from a certain height and one that's thrown horizontally outward also from the same height and then the question of course is which ball will hit the ground first and of course the ground should have been flat not quite the answer is they will both hit the ground at the very same time and sometimes that seems a little puzzling because intuitively we would think that this ball which travels a greater distance would take a longer to hit the ground before the ball that just gets no drop straight down and the reason why that is not the case the reason why they hit the ground at the very same time is because the motion in the X direction and the motion in the Y direction so the horizontal motion of the ball and the vertical motion ball are completely independent of one another notice in the horizontal direction there's no forces acting on the balls so this ball will stay stationary in the X direction simply fall down in the Y direction this ball once thrown out to the right at some initial velocity in the X direction it will no longer feel a force in the X direction and so the ball will simply maintain the same velocity in the horizontal direction in the vertical direction the Y direction both balls feel the exact same force they feel the force of gravity so on the Left ball we have a force due to gravity and on the right side we have a force due to gravity so both balls feel the exact same force assuming that they have the same mass and so therefore they're being pulled down or accelerated downward at the very same rate you can see that the velocities in the Y Direction are the same at the same time interval and you can see that therefore they will hit the ground at the very same time so what can we learn from this well first of all we should learn that the time in the air for ball number 1 is equal to time in the air for ball number 2 so that is really important later on when we start doing problems and examples that concept is extremely important so the time in the air for any projectile no matter what happens to it only depends upon the vertical velocity and the vertical forces also we should always keep in mind that the motion in the X direction so we talk about the horizontal direction is completely and I mean completely independent of the motion in the Y direction of course that would be the vertical motion so why did I take the time to write that down well it's a really important concept so in all problems I'm going to do with projectile motion you can look at the horizontal motion in the vertical motion completely independent as they have nothing to do with each other the only thing is that the time in the air depends upon how long it takes for the object to hit the ground in a vertical direction so let's now talk about how we describe the equations of motion in the two dimensions so for the horizontal since there are no forces acting on that in that direction there's no gravity in the horizontal direction we can simply say that the velocity in the X direction is simply equal to the initial velocity in X direction and it doesn't change so whatever the initial velocity was in the X direction it will maintain that velocity throughout its entire motion doesn't change notice that the arrow in the horizontal direction doesn't change that represents velocity in the X direction the distance traveled in the X direction is simply equal to the initial velocity in the X Direction times the amount of time that the object stays in the air which is determined by the vertical motion only alright on the vertical motion the velocity in the Y direction is equal to the initial velocity in the Y direction plus the acceleration times time and in this case we can probably just say that the acceleration for projectile will be of course the acceleration due to gravity and that's in minus 9.8 years per second squared notice that it has if it has no initial force in the Y direction on V sub I simply equal to G times T and for the position we could say that Y is equal to initial position the Y Direction plus the initial divider action times time plus 1/2 G T squared and of course that came from the equations of motion so those are the two ways in which we look at motion of projectile horizontally and vertically and we keep them completely separate so there's a nice little introduction of how to look at two-dimensional motion and how we look at X&Y motion completely independent and that's the basis on by which we're going to solve all problems for projectile motion