In this exercise, we have ah, block A that has a mass M and an initial speed V and two blocks B and C B has a mass to him and CMS em and they are initially at rest and block a collides with block B And then block V collides with Bloch si and we have to find what are the final speeds of A, B and C. So we have to consider that the three collisions, Actually, the two collisions that happened are elastic. So let's find out, um, what the speeds are by using both conservation of energy and conservation of momentum. So the first collision is the collusion of A with B. So the initial, uh, energy of a is M. V squared over two and my concern conservation of interview This is equal to the final energy of A, which is M times V. A square. Over to V is the the speed of the block a plus the mass of the block to which is to him times the speed on the block B. Which is we be. I'm gonna call VB over to So this leads two. If we just cancel the twos out and so And the the EMS as well. This leads to V squared is equal to the ace Where close to V V squared. Okay, so this is one of the equations and then we have this concern, conservation of energy, and then we have to use conservation of momentum. The initial momentum off a is M. V. The final momentum is M v A. I'm assuming that va is moving to the right. But that is not the problem. It's not, uh it doesn't restrict our options in the end, because if V is actually pointing to the left, then we're gonna get a minus sign. And the final momentum of B is MPP. So from here we have the V is equal to V A plus VB. I'm gonna isolate V A. So I have the three a is equal to the miners. VB So this is the second equation we have and I'm gonna just love this into the first equation. So the first vision is the square is able to be a squared and these female sgb plus two times vb I swear So the square is equal to the squared minus two v vb square VM Sorry, because we be square plus two VB square. So is that the V's Cancel out each and we get to, Ah, one of the babies do as well So have to be. It's about a three d d. So we get that VB is equal to two times V over V over three insert. This is the speed of the block V after, uh, after Block A heads it and now confined the speed of the block. A. So that's just V amenity bees, which V minus two Viewer three That's minus V or three notice. That's since there's a minus sign here than a The Block A is moving to the left, and it will not collide with the other blocks anymore. So this year is the final speed a block A. Okay, uh, now we can move on to the second collision between about being black sea, so it's B B with C. Again, we have to use conservation of energy. So we have the initial speed, which is just outside of the initial energy, which is M V C B squared over two, and this is equal to ah, the final area that's in actually the massive look these to him, so I should everything to him here. So it's the method. Luck be times the final speed of B square. That's capital T B divided by two plus the massive block C, which is just M times the finals beat of C squared over two. And from here we just get that too. Uh, the M skin. Salo's so does too. So we get the to be be square is equal to capital VB Square. Actually, there's two years to capital B B squared plus B C square, and I'm gonna save this equation and now use the conservation of momentum. So from consideration when that's when we get a to M V B is equal to two m sir, I should add that the initial momentum. Miss, just lower case V B, This is able to to em capital Phoebe plus M b c. So again, the EMS cancel out and we get to the B is equal to two capital VB plus V c. And I'm gonna isolate the bees we get. The thebe is equal to lower case V B minus V C word shoe. I'm gonna take this value of the B end, Plug it into the laying in the first boots. I have to V B Square, which is able to chew times Capital VB Square. So it's this is or case vb times V C Square plus V C Square, so get to VB. Squared is equal to two V b squared, minus two times VB V C plus B C squared over two plus B C square. So the two V B squared cancels out. One of these devices do as well. So you get to VB is equal to three halves of the sea, so V C is equal to four thirds of VB. You know VB Lorca's Phoebe. Um, we have already calculated it, so it's people to to be over three. Let's just plug it in here so have four thirds times two thirds of V. So this is 8/9 of the This is the final speed of the Block C. And I can company the finest Peter the block be going back to this equation right here to have vb. VB is equal to lower case V B minus this year or two now, Phoebe, Laura case. Phoebe is just two thirds of V while the sea is eight v overnight. Then I have to multiply by two. So he gets, um, 6/9 off he That's just two thirds of the minus four V or nine. So this is equal to to view everything. This is the final speed of the block B in the end, to a question.