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Hi there.
00:01
So for the first part in this problem, we are asked to calculate the kinetic energy of a carb with a mass that is given, and that mass is equal to 1 ,200 kilograms, and it is moving with a velocity of 15 meters per second.
00:20
So the question in this case is to calculate the kinetic energy.
00:23
So we know that the kinetic energy is defined as 1 divided by 2 times the mass of the object times its speed square.
00:30
So we just need to simply substitute those values 1 ,200 kilograms for the mass times the speed that is 15 meters per second to the square.
00:40
So using our calculator, we obtain a value of 1 .35 times 10 to the 5 jules.
00:56
So that's a solution for the first problem in here.
01:03
Now, for the second problem, we are asked about to calculate the gravitational potential energy of a person with a mass that is given of 60 kilograms at the top of a 10 meters flight of stairs.
01:20
So we are given the mass in this case, and that mass is equal to 60 kilograms, and the height is also given, and that height is equal to 10 meters.
01:34
So with that said, we need to calculate the potential energy.
01:38
We know that the potential energy is defined as the mass times acceleration due to gravity times the height.
01:43
So that will be 60 kilograms times acceleration due to gravity that on earth is 9 .8 meters per second square, that times the height that is 10 meters.
01:52
So using our calculator, we obtain a value of, 5 ,880 jules.
02:03
So that's a solution for problem 2 in here.
02:07
Now for problem 3, we are asked about well, we are told that 200 grams model rocket if subserved to rise to a height of 100 meters.
02:28
So remember that we can pass the mass that is in grams to kilograms, so that will be 0 .2 kilograms.
02:36
And so, okay, so rise to that altitude above the ground after launch.
02:41
So what was the launch speed of the rocket at the ground? so for this we need to use conservation of energy.
02:50
We know that all of the kinetic energy, the initial kinetic energy, was converted into potential energy, which is the mass, times acceleration due to the gravity, times the high, so since we have this equality in here, we can cancel the mass of this, then we can solve for the speed because that's what we are asked for.
03:12
So if we solve for that, we will have the square root of two times the acceleration due to gravity times the height.
03:19
And now we just need to simply substitute the ballast in here, two times 9 .8 meters per second square.
03:27
This times the height that is 100 meters.
03:30
And then we take the square root of all of this.
03:33
So using our calculator, we obtain a value of 44 .3 meters per second.
03:45
So that's a solution for problem three in here.
03:49
Now, for problem four, tell us that a 70 kilograms pole balter converts the kinetic energy of running at ground level.
04:01
Into potential energy to clear the cluster part at a height of four meters.
04:06
So we are given the mass that is 70 kilograms, and we're given the height that is four meters.
04:14
And we're told that all of these, well, all of the kinetic energy is transformed into the potential energy.
04:24
So with that said, we are asked about what is the minimum velocity that he must have when he takes off from the ground, in order to clear the bar.
04:34
So in this case, we need to use the same definition as before.
04:37
This one in here, that, well, we know that this comes from the conservation of energy, which is the same that we need to do in here.
04:46
So the speed is going to be just simply the square root of 2 times acceleration due to gravity times the height.
04:52
As you can see in here, this quantity doesn't depend on the mass.
04:58
So that will be 2 times 9 .8 meters per second square that times the height that is equal to 4 meters.
05:08
So taking the square root of all of this.
05:10
So using our calculator, we obtain a value of 8 .85 meters per second.
05:22
So that's a solution for problem 4 in here.
05:27
Now for problem five, we are told now that a 10 kilograms monkey swims on a bind from a point, which is 40 meters above the jungle.
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So we are given some initial height of 40 meters.
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And well, its mass is also given.
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Its mass is 10 kilograms...