in this video i will talk about the motion of a ball when it is tossed up so we have a ball here please let's say this is a ball here and the ball is thrust up upwards and a person who throws the ball upwards the height from the ground this is the ground level here the g stands for the ground and this is the height given the height of the ball is one meter so it is thrown upwards from one meter height so let's look at the the motion when it is thrown upwards with a velocity of 10 meter per second what happens is the velocity starts decreasing the magnitude starts decreasing and when it reaches to the peak the velocity at this point is zero but the particle is still accelerating and the direction of the acceleration at any point is always in the downward direction here the velocity is in the upward direction and the acceleration is in the downward direction when it starts descending or when it starts falling down in that case the velocity is in the downward direction and the acceleration is also in the downward direction what does it mean when the velocity and acceleration are in the same direction that means the magnitude of the velocity or the speed starts increasing so you see here it will keep increasing the the velocity the or the magnitude of the velocity the speed starts increasing because the velocity and the acceleration are in the same direction and in this case when it is thrown upward the velocity is in the upward direction and the acceleration is in the downward direction as these two are in the opposite direction that means the magnitude of the velocity or the speed starts decreasing so the the velocity at this point is given which is 10 meter per second and the height from which it was thrown is given one meter and now from these two information we have to find out what is the maximum height we need to the ball reaches two we have to find out the height from the ground okay that's the one thing we have to find it out and how long does it take to reach to the the peak how long does it take to reach to the peak and then come to the ground the total time what is the speed of the ball at the point b what is the speed of the ball at the ground so we have to find out all the information let's start now so in this case the acceleration due to the gravity the g value is constant it's not changing and which is the magnitude is 9.8 meter per second square that's the magnitude value all right so so a is the starting position and the ps stands for the peak when it ball reaches to the peak so first we're going to consider the motion from point a to p that is from a point to b point and let's find out this height here this height here so we know the velocity at this point is zero so i'm going to use this equation here v square is equal to v naught square minus 2 gs and why because we know the velocity at this point and i know the velocity at this point so we should be able to solve for the height so here v squared and always remember this is the final velocity and this is the initial velocity g is the acceleration due to gravity and why i'm putting negative sign here the reason is when the ball is moving upwards the g the velocity is upward and g value is in downwards okay so the velocity and the acceleration are in opposite direction that's the reason i'm putting the negative sign here or in general when you throw an object upwards you use the negative sign here the acceleration due to gravity and this height h is the height from a to p this is the height so let's plug in all the values here this is the final velocity the v is the final velocity or the velocity at the point p or the velocity when it reaches to the maximum height and you know what the value is the value is zero so that's zero here and the velocity the initial velocity at this point is 10 and s squared here minus 2 g the value of g is 9.8 that's the magnitude value h is from h a to p okay now if you solve it what you get is it's uh this height is five point one zero meter so the total height from the ground to the maximum height is reached is this is 5.1 and we already know this height is 1 meter so the total height from the ground here this is h here is 6.1 meter so found out the total height now the next thing it asks you how long does it take to reach to the peak here okay so now let's find it out the time now the time to go from point a to the point b so again we're going to use this equation here v equals to v 0 minus g t and for the same reason we have used the negative sign here whenever we considered about the motion while the ball is going up or your negative sign here and this is the final velocity or the velocity at the peak and that velocity is zero and this one is 10 meter per second minus g value is 9.8 and the time is time to go from a to b this time here just tells you a to b so from this point a to b now let's solve it now so once we solve for the time we get one point zero two second so time the time the ball takes to go from a to p is 1.02 second so now let's find out what how long does it take to go from p to b the point b is right at your hand level okay or how long does it take to come from the maximum height to the level of your hand so let's calculate this one so that we call the time to go from p to b from p to b from symmetry so that the the time it takes from a to p is a takes exactly the same time to come from p to b so it also takes about the same time here not about it takes exactly at the same time if you ignore the air resistance okay so the time to come from p to b is exactly the same time it takes from to go to from a to p which is 1.02 second all right so now the total time it takes from a to come back to b or time to a to b and then b to p the total time it takes to come to the hand level will be 2.04 second first you calculate the time it takes to go from a to p to the peak and then from p to again b so which is 1.02 plus 1.02 and you'll get 2.04 second that means that it takes 1.02 second here and 1.02 second here if you add them together you'll get 2.04 second and then now let's find out what is the speed of the ball at this point b if there is no any air resistance then the speed of the ball at point b will be exactly the same as the speed of the ball at point a or the at or the speed at which it was thrown upwards okay so the speed at the point b is exactly the same as the speed at point a and remember it holds for at any point the speed let's say at any arbitrary point the speed at this point will be exactly the same as the speed at this point or the speed or the speed at this point will be exactly the same at the speed at this point okay so the speed at which the ball passes our hand will be exactly 10 meter per second because it was thrown with the 10 meter per second and you can also calculate this one if you are interested calculating mathematically you can do it and how do you do it you can simply plug in v equals to v 0 plus g t and i will tell you what what it is this is the the final velocity or the velocity at point b and this is the initial velocity v zero which is zero y t zero because at the peak value this is zero so let me write down here v equals to v 0 plus g t and this is the velocity at the point b here when i say at this point b here and v 0 is the initial velocity here i'm considering the motion from point p from point p to point b and this initial velocity here at this point is zero okay so from this point to this point so this is zero plus g value is nine point eight and time is one point zero two if you multiply them together you will get to be ten point ten meter per second so you can solve either way so we see now the velocity at point b is exactly one point or 10 meter per second now let's find out how long does it take to reach to the ground or the total time it takes to reach to the ground so now let's consider the motion from point p to the point to the ground or uh it should be the ground here let me make a slight changes here this would be the ground okay so i'm considering the motion from point p to point g here and i'm going to use this formula here h equals to initial velocity times t plus half gt square what is h here the h is the total height and we already have calculated this side which is 6.10 and this is the initial velocity the starting velocity or the velocity at point p or the velocity at the maximum height which is zero so this term zero half and the here the plus sign means the ball is coming downwards when you throw a ball upwards then you will use the negative sign and the one when the ball is falling down then you will be the positive sign half g value is 9.8 and the total time it takes from p to g is t here time p plus f p to g here and if i solve this time then it is 1.12 second so the total time it takes to ball to come from p to point g is one point two one two second so how long does it take the ball or how long the ball remains in the air so the time from a to p and then p to g that's the the total time the ball remains in the air so we just calculate we already have calculate the time from a to p from a to p which is 1.02 second and we just calculated the time from p to g which is 1.2 second so this time is 2.14 second okay and there is an alternative approach to calculate the time so if you are interested just go through this approach here and i'm not going to explain it here so this is another approach now what i'm going to calculate is what is the speed of the ball when it reaches to the ground the speed of the ball the speed of the ball can be calculated using this formula here and this is the motion from p to b what is p here the p is the peak sorry this has to be again g not b this has to be g here okay so the motion from p to g i'm going to use this formula here and what is v here that's the final velocity or the velocity at the ground or simply call the speed at the ground and this is the initial velocity or the velocity at the point p which is zero 2 g h and if i solve for v g it will be a square root of 2 g h we know the value 2 is a constant the g value is 9.8 and just calculate height which is 6.8 if i solve it then this is 10.93 meter so the ball hits the ground with 10.93 meter and remember this has to be greater than 10 meter per second because the ball was thrown 10 meter per second so when it reaches to the point b it should be 10 meter per second and then it keeps accelerating so the the magnitude of this uh the velocity or the speed at the ground has to be greater than 10 meter per second which is 10.93 meter per second here the unit is again missing 10.93 meter per second so this is it for the the motion of a ball when it is just tossed upward okay so again if you have any questions let me know and at the end do not forget to like share and subscribe the channel thank you very much