in this video I'll talk about car owners hill so we have a car at the top of a hill and it is all opposed to run out of the gas the gas station is on to the another peak of the hill now the question is how much the velocity or the kinetic energy this car has to be in order to reach to the the gas station and we assume the entire system is under a conservative force the conservative force or the conservative field is this field in which the total mechanical energy of the system is conserved just like a gravitational field the total or there is we assume there's no friction force as well so how are you going to solve this problem if this car does not have any velocity or any speed that the maximum height it can get is to the side because when you release all the potential energy will change into the kinetic energy and again this kinetic energy will change into the potential energy so the maximum height it can get to is this height so you must need some additional a speed that needs to be comported to the car so that it can reach to the gas station and how much is the speed required at this point or at all or in other words was the minimum speed required to make this car to get to the gas station so let's find it out so the height of this hill onto which the car is is 20 meter and the gas station is at the height of 30 meter but the if this is a conservative field and the total kinetic energy at any point must be exactly the same so in order for if this can reach to the gas station under the conservative force then the total energy at point one has to be equal to the total energy at point two when I say that total energy that it includes the kinetic energy and the potential energy or gravitational potential energy so so the total energy at point of one is equal to total energy at point two this is coming from the conservation of energy the total energy at this point is kinetic energy plus potential energy even at this point two the total energy any clothes kinetic energy plus potential energy the kinetic energy at this point is half mass the minimum squared Y I'm adding V minimum because we're trying to find out the minimum speed that makes this car to go to the gas station and the potential energy our gravitational potential energy that at this point is MGL or just likely to make a note of this one the gravitational potential energy the gravitational potential energy the formula is equal to M G H M is the mass Z the acceleration due to gravity s is the height so from this ground level to this height similarly the kinetic energy at this point at point two is zero and why is it in general because the car just makes it to thee in the gas station or just birnley riches to be the gas station so there is no speed at all so it just gets there so that's why the the kinetic energy at that point is zero and the potential energy at this point is M gh2 which is this height so now the mass mass and this mass cancels out so it is entirely independent of the mass and if we solve for the speed what we get is a square root of 2 G that's 2 minus a strong so this one turns out to be a very simple equation so this is what it is it's 2 minus H 1 2 G value is 9.8 it is 30 meter here and that's what is 20 meter and if we do the math then the minimum is speed is 14 meter per second and here we assume there is no friction force at all okay so with this minima spear the car just reach to this gas station okay now I would like you to do one more thing here what is the speed of the car at this point which is 25 meter from the ground calculate the speed at the point which is 25 meter from the ground and write down your answer in the comment section below so this is it and I can if you have any questions write down your questions in the comment section below and do not forget to Like share and subscribe this channel thank you very much