00:01
Hi, in this question it is said about that what is the final velocity when an object is thrown vertically upward direction? so suppose we have considered an object that has been thrown vertically upward direction.
00:19
Suppose see, this is the ground.
00:22
Suppose this is the ground or the surface.
00:26
Now from ground an object has been thrown vertical.
00:30
Upward direction.
00:32
So vertically upward direction means along this direction, that is positive y -axis along positive y -axis, right? so with some initial velocity.
00:45
Suppose, let us consider the body has been thrown or projected in vertically upward direction, that means 90 degree to the horizontal.
00:56
So that plus y axis with some initial velocity u with some initial velocity u.
01:04
So now the question is that what will be the final velocity after reaching the maximum height? suppose this is the maximum height a.
01:15
Okay? and suppose this is the ground point g and ag we have considered as the maximum height h.
01:25
So ag is equal to the maximum height.
01:30
That is denoted by capital h.
01:34
So what will be the final velocity of the object after reaching the maximum height? that means after reaching this point a.
01:45
So now we have to find out the velocity.
01:49
The final velocity that is denoted by small v.
01:52
Generally we denote the final velocity by small v.
01:56
So that we have to find out.
01:58
So now this question is based on the.
02:00
Principle of energy conservation the total energy that is the total mechanical energy is equal to the sum of the kinetic energy and the potential energy of the object to the principle of conservation of energy the energy must be conserved at each and every point throughout its whole path the mechanical energy should be conserved should be remain constant or same, right? that means we have to apply this concept to find out the final velocity.
02:40
Now see when the object is at ground, that means when the object is just projected from ground, that is at g.
02:51
So we can see that at point g there is no height.
02:56
At point g there is no height because the point is on the ground surface that means height is zero because we have to take the height from the ground okay because the motion is directed in upward direction upward direction so we have to consider the height from from the ground point along plus y axis right so at g the height is zero.
03:25
So when the height is zero, the gravitational potential energy that we know is equal to mg h, the gravitational potential energy, okay? where mg is the gravitational force and h is the displacement, that is the height from the ground, right? this is known as the gravitational potential energy.
03:46
So it will be zero.
03:48
So when the gravitational potential energy is zero, the kind of energy must be maximum okay because we know that my mechanical energy is the sum of kinetic and potential but when this potential is zero so that the total energy total mechanical energy must be equal to kinetic energy to maintain the principle of conservation of energy so at g kinetic energy is equal to maximum okay and that is equal to half m u square where u is the initial velocity okay now see what about maximum height so when the body when the object will reach the maximum height okay when the object when the object reaches the maximum height suppose in this case at point a okay so it will get displaced by a maximum height.
04:57
So what is the displacement here? the displacement is equal to capital h...