00:01
When sandbag is released from the balloon at a height of 31 metre, it does not, suppose the balloon was rising up like this and sandbag is released here.
00:19
But because of the inertia, the sandbag does not fall down instantly because of inertia and its initial upward velocity which is same as the upward velocity of the belly.
00:32
Balloon, the sandbag raises rise to some upward distance till its velocity becomes zero, upward velocity becomes zero, then it falls down.
00:50
So first we need to find out the upward distance it traveled after it is released and before it starts to fall.
01:02
Because after it is release from the balloon, it rises some distance upward.
01:09
So to calculate this distance, we need to use the equation v square minus u square equal to 2as for the upward motion, upward motion of sandbag, right? so final velocity of the sandbag is zero.
01:44
Say because before sandbag starts to fall, its velocity is zero.
01:49
Then it falls.
01:51
And initial velocity of the sandbag is same like the velocity of the balloon, which is constant 6 .5 meter per second.
02:02
And the acceleration is equal to minus 9 .8 meter per second because in the upward direction, the acceleration is negative.
02:15
So we put all the values is 0 squared minus 6 .5 whole square is equal to 2 minus 9 .8 multiplied by s.
02:30
This gives s as 2 .15 meter.
02:37
It means before falling, before falling, down the sandbag travels an upward distance of 2 .15 meter.
02:57
It means its maximum height means from where it falls is equal to the height when it was released.
03:10
This is 31 meter and the upward distance it travels before it falls down.
03:18
This is 2 .15 meter.
03:20
So this this is 33 .15 meter.
03:25
This is the maximum height, right? and it means this is more than 33 meters.
03:40
This is the answer of part a, right? now we'll come to part b.
03:58
Say what is the speed of the bag just before it lands when it is released from 31 meters? as we have already calculated in part a, when the bag is released, say, from 31 meter, it actually starts to fall from a height of 33 .15 meter.
04:38
Height of 33 .15 meter because it raises 2 .15 meter upward.
04:45
Right so now before it starts to before the sandbag starts to fall down its velocity is zero right because it raises up then it stops and fall down finally before it falls down falls down or we can say just before it falls down its velocity or speed is zero it means its total energy is equal to its potential energy, which is mgh.
05:30
Now when sandback falls and it reaches the ground, just before it hits, just before it hits the ground, hits the ground, right? its height is zero.
05:55
Height is zero.
05:57
So it means its potential energy is zero.
06:03
So its total energy is the kinetic energy.
06:08
So total energy is equal to kinetic energy is equal to one half mv square...