in this video i will talk about the intersection collision that means the collision of two cars at the intersection so two cars this is the car one and there's the car two and both cars are moving towards a junction or an intersection and they collide so after collision they move at an angle here and this angle is given which is 20 degree and the velocity so after collision then the two cards are now locked together and they move with a common speed of 30 meter per second the direction is also given which is 20 degree so from this information we need to find out what is the speed of the car one and what is the speed of the car too or who we're driving faster okay so how do we going to do it again what you need is just an understanding of the conservation of linear momentum and at the same time you should be able to resolve a vector a velocity or into two rectangular components okay let's get started so the mass of this car is 1000 kilogram and the mass of this card is 1500 kilogram and after collision both move together they get locked and move with 30 meter per second and the angle is 20 degree with respect to the first car direction so we now need to apply the conservation of linear momentum and this is called a perfect inelastic collision this is inelastic collision when the two cars are locked together that means this is an inelastic collision okay so let's apply the conservation of linear momentum and i will tell you one thing whether it is a elastic collision or inelastic collision the total momentum is always conserved so now we're going to apply the conservation of linear momentum along the x-axis and then we'll apply the concentration of linear momentum along y axis so we'll just apply have two equation one along the x axis and then another along the y axis okay let's find out first along the x-axis what's the momentum of this car this car is already moving along x-axis what is the what is its momentum the momentum is mass times velocity it's which is m1 times v1 this card is also moving but it is moving only along the y direction this does not have any component along the x-axis so the momentum of this car along the x-axis is zero so we have only this momentum before collision this is before collision let me write down here oops momentum before collision before collision and this is momentum actor collision okay so and it has to be equal so after collision what is the momentum so these two cars moving together with a common velocity of v and the component of its velocity along the x-axis will be v cosine theta and this component will be v sine theta or i can write it down that this one would be v cosine theta and this one will be v sine theta so now along the x-axis what is the total momentum that in order to calculate the total momentum we need to take the total masses these two car is moving together so the total mass is m1 plus m2 and along the x-axis the velocity is v cosine theta so m1 plus m2 times v cosine theta is the momentum along the x-axis exactly what it is yet m1 plus m2 times v cosine theta so we can solve for v1 which is the speed of the car first so v1 will be we're just dividing both sides by m1 theta is known so it is 20 degree mass both car mass is known this one is thousand kilogram this is 1500 kilogram so this car was moving at 70.5 meter per second now let's find out what is the speed of this car now how do you do that now you might have an understanding in order to find out the speed of this car we need to take the momentum equation along the y-axis so let's write down the momentum along the y-axis what is the momentum of this card along y-axis think about it the momentum if this card along y-axis is 0 because it is moving only along the x-axis and the momentum of this car along y-axis is m2 times v2 okay so now let's see it now this is before collision and this is after collision so this momentum is m2 v2 and this as this one is moving at an angle this has a component along y-axis and we already have mentioned the velocity component along y axis is v sine theta so what is the momentum of the two cars together along y axis the mass and the mass is m1 plus m2 and the velocity component which is v sine theta so if i write down that's exactly here m1 plus m2 times v sine theta and again interested in solving for v2 so v2 will be m1 plus m2 divided by m2 v sine theta m1 is 1000 kilogram m2 is 1500 kilogram and plugging all the values this is 17 1.1 meter per second so which is significantly smaller than the v1 so this car was definitely over speeding and this is some this is how the police officer also investigate an accident situation as well and they can find out with a certain information which car was over speeding just from all the information okay in this case this portion is moving way higher than this person so this is it for this intersection collision problem again if you have any questions any suggestion any comments please write down in the comment section below and do not forget to like share and subscribe the channel