in this video I'll be talking about the motion of a projectile when it is fired horizontally from a height so let me draw the picture here let's say you are let's say you have a project I'll and you fired the projectile originally from this point and it is fire horizontally and this is the ground here now in this case we'll be calculating how long does it take to reach to the ground and at what angle it hits the ground so we called this as an origin and let us say the velocity of the object at which it is fired is V zero X that's the horizontal velocity at which G that's footage fire the motion this will be the path of the projectile let's say at any point the object is at this point we assume the location is X Y so this one will be the why we assume this isn't foraging so this distance or this distance is X and this is y so now let's call this height the height this is the ground the height of the building or tower from which you fired is H so in this case I let me write down the object is we're going to leave for my height edge so so the force of gravity is acting only along the vertical motion sort of so force on this particle or here is acting only along this motion here in the particle motion there is no force acting along the x axis like what does that mean that means the horizontal velocity at each point is exactly the same what is changing is the important versity as the particle is a falling freely under gravity IFS velocity will keep increasing along the particle motion while the horizontal velocity at this point will be exactly the same so it doesn't matter where you take at this point this point or here even here the horizontal velocity the horizontal velocity will be exactly the same which is V zero X but the vertical velocity will keep increasing so let me call that velocity as V Y or at this point is the V Y so horizontal velocity it does not change its a bit that means the acceleration along the horizontal axis or along x axis is zero there is no acceleration because the velocity is constant so now let's first calculate how long does it take for the particle to reach from this point to this point okay let's calculate that one the time to which to the ground so in this case in order to calculate this time we'll be talking of the motion along the y-axis all the motion is now that conserving is along the y-axis let's use this formula here and remember along y axis what is the initial vertical velocity at this point there is no initial vertical velocity the only you velocity is along the x axis there is no velocity at this point along the x axis so V 0 Y is 0 that is initial vertical velocity is 0 so we're going to use the formula so in this case the s is the vertical height so in this case the vertical height is H and the V 0 is the initial vertical velocity which is 0 half and here I'm writing that's half GT square this is H here so we can find the time here the time and I'm calling this time as a kettle T just to make a difference of the time they'd given wife to edge over G square root of G this is what you get over solve this equation ok this is the time to whisk to in the ground this time now let's calculate what is the horizontal range when I say horizontal plane that means the distance from this point when it hits the ground that's the horizontal range let's calculate that for this one we are again using the motion along the x axis along the x axis so our motion all the parameters which huge here will be along the x axis I'm going to use the same formula t plus half ay T Square okay now along x axis the expiration is zero there is no any acceleration because there is no force acting along it and the initial velocity is simply given as V zero X so what you get is now and we already had calculate at the time here this time the S is given by the horizontal range the initial this is the initial horizontal velocity which is V zero X and the time is given by 2 H over G as there is no acceleration this term would be 0 so far it's given by V zero X a square root of two HG the horizontal velocity is given you can simply find out the horizontal range that's how you calculate the horizontal range now let me calculate the the vertical velocity at any time that means what is the velocity at this point or this point at this point at any time if you know the time you can calculate the the vertical velocity let's do that vertical velocity at any time gene okay so how do you calculate this one so remember the kinematic equation V is V naught plus G times T and again along Y axis so though at any point I can write down let's say this is the V is the V Y here and the initial vertical velocity is zero remember when the projectile is fired we fire horizontally so there is no component alone along the the y axis or along a vertical axis so the initial vertical velocity is zero plus G times T and this time is at any point and at any time T so this is how we calculate the vertical velocity this is simply equal to G times T so if you know the time we can calculate the the vertical velocity the net velocity that we calculate the net velocity now the total velocity at any time or at any moment at any point let's go back at this picture again at any point at any point the object has two velocity one is a horizontal velocity and the other is the vertical velocity the horizontal velocity is constant which is given V zero X for the vertical velocity is changing if you I so the total velocity is given by this gives you the the magnitude of the total velocity let's say this angle is hater this is the V total so the total velocity so the total velocity is simply given by if you look at this triangle how do you calculate in this triangle here this triangle this is a horizontal velocity this is the vertical velocity so the total velocity would be equal to V squared plus V zero Y square so the total velocity can be given by because we know the horizontal velocity is given and the vertical velocity is given by G times T so this is the total vertical velocity at any time we can also calculate this angle theta this angle theta here to how to calculate the angle let me write down here angle at any time so if you look at this triangle again this triangle here that turns and theta tangent theta is given by the vertical velocity divided by the horizontal velocity theta so that anytime would be equal to tangent universe the vertical velocity divided by the horizontal velocity that's how you calculate the deep Engel at any time T okay so I do not want you to memorize all the formula so all you starts from these kinematic equations and starts calculating all the other quantities that you do not know so do not memorize this formula