in this problem I'll talk about the billiard balls collision at an angle it's not a hidden collision rather it is a collision at an angle so we have one billiard balls which is moving with a velocity of 5 meter per second and then an identical ball is sitting here at rest the when the ball hits this second a ball at an angle then the after the collision the first ball starts moving at an angle of 40 degree with respect to its original direction and the second ball which was at rest and starts moving in the other direction and now we have to find out what are the speed of the balls find it it should be speeds here so what are the speeds of the ball after the collision okay so we now have to find out V 1 F and V 2 F again V 1 I means the velocity of the first ball and I stands for the initial velocity or before collision and the second ball as it is hitting rest the most velocity is 2 in general meter per second and the V 1 I means velocity of the first ball and the ephah stands for after collision or the final velocity so we have given this angle as 40 degree and I would like you to keep in mind that when the two identical balls are just like a pool when you play a pool when the two balls hit each other at an angle then after the collision the angle of separation is 90 degree so this angle is always 90 degree there are two conditions the one is elastic collision and the second condition is the mass of the two balls should be exactly equal if it is then the angle of separation is always 90 degree let's give this one in wine so this angle is 40 degree if this angle is 40 degree you know what this angle has to be now what is it 50 degree so this angle is 50 degree and remember so in order for this angle to be 90 degree the mass of the two balls has to be equal and this has to be elastic collision okay so we already had calculated this one to be fifty degree fifty degree and now let's use the conservation of momentum and we have conserved we have to write down the concern of conservation of momentum along two axes first along the x-axis and then we will write down the conservation of momentum along the y-axis it doesn't matter what kind of collision is this the momentum along x axis and along Y axis is always conserved okay so let's start with the x axis so the initial momentum before collision I'll just write it down the total momentum before collision total momentum before collision it has to be equal to total momentum after collision okay so now let's calculate the total momentum before collision so this mass is moving along the x axis so what is the momentum the mass times velocity which is em V 1 I this has to reach X here so this has to be I okay so M V 1 I and now what is the momentum of the second ball here the momentum of this ball is 0 why because it is sitting stationary it is at rest and now we'll calculate the after collision so after collision this ball is exactly not moving along the x axis but rather at an angle okay this has to be again let me make one view 1/2 cosine theta so this ball and I mentioned it is moving at an angle so a component of this ball along the x axis are the velocity of this ball along the x axis is the u1 F cosine theta okay and the component of this ball along Y axis will be if you want to have sine theta always remember if this is the angle this is angle this has to be the cosine and this will be the sine component the v1 F cosine theta and similarly we are going to be solve this one into two components one along the x axis and another along the y axis as this angle is alpha so the velocity the component of velocity component along x-axis will be v2 F cosine alpha Y cosine alpha because this is the angle alpha and this component will be v2 F sine alpha if you just can draw this Freebody diagram or the direction of the velocity along the x axis and y axis then you're good then it is pretty simple things to do all you have to do is to resolve this velocity into two components this component will be cosine component and this will be the sine component similarly resolve this one into two components one along the x axis and another along the y axis this component will be cosine and this component will be sine this is okay so now let's calculate all the momentum after the collision so after the collision the momentum will be v1 F cosine theta so this is M v1 F cosine theta and the momentum of the second ball will be M v2 F cosine alpha because we have two velocities along the x direction now the one is coming from this ball and the other is coming from this ball the first of all and the second one together now and as this two are they equal masses this mass mass cancels out okay so v1 F cosine theta is given which is 40 degree v2 F cosine alpha we already have calculated this is 50 degree so it's just plugging the value of cosine 50 40 degree which is point seven seven and cosine 50 degree is point six four so this is the total momentum along the x axis the same thing we're going to do the total momentum after the total momentum along y axis so the initial total momentum what is the momentum of the Paul along y-axis it is zero because this ball is moving along the excellent x direction and if it or in other words if you take any component along y axis this angle is 90 degree so cosine 90 degree will be in general so this abala do not have doesn't have any component along y axis similarly the momentum of this ball along Y axis is zero so the total momentum initial momentum along x axis is exactly equal to zero this is before collision and now let's take a look after collision after collision the first ball has a component of man at the V 1 F sine theta and this one here has in v2 F sine alpha so the component of the first of all are the momentum of the first part will be mass times this velocity that's what it what I've done here mass times V 1 F sine theta and the mass V 2 f sine alpha and the negative sign here because this one is has the component in the opposite direction that's the negative sign so now I'm going to simplify this one M is the negative sign here and this is zero so I'm taking this one to the other side M U and F sine theta then we'll help M we do have sine alpha mass mass cancels out and then if you solve for the v1f what you get is view and F is now equal to V 2 F 1.19 so there is a relation now between the V 1 F and if you have so what I'm going to do now I'll plug this V 1 F into this equation ok so let's do that now so I'm just plugging you see now here five we have five this is five year and instead of u1 f I music v2f 1.19 we he to f1 19.7 seven v2f 164 and then solve it after solving what I get is three point two one meter per second that's the velocity of this second ball once we know the v2f then we can plug this back into this equation and solve for V one half and we solve for the v1f which is three point eight two meter per second so that's how we calculate the speed the ball after collision so just by using the conservation of momentum we were able to solve the collision of the balls after the collision okay so this is it for the billiard balls collision at an angle again if you have any questions any cessations any comments please write down your comment suggestion or anything in the comment section below and at the end do not forget to subscribe the channel thank you