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we finished going over the first of three things you need to create a particle simulator first we have formulas that describe how particles will move based on the laws of physics in this video we'll develop formulas that describe how particles will behave during collisions if velocity is perpendicular to the floor at the moment of collision and the collision is perfect then the velocity reverses in the real world its direction reverses and the magnitude is slightly reduced due to friction as we introduced in Lesson one we can model the frictional losses by multiplying by a factor that measures the elasticity of the collision so a V is the downward velocity before the collision with the floor then the velocity called V prime after the collision is given by V prime is equal to negative e times V here E is the elasticity a number between 0 & 1 and the minus sign indicates the direction reverses after the collision if equals 1 the collision is perfect and no energy is lost if E is less than 1 then some energy will be lost but what if the velocity makes an angle with the floor let's observe what happens on video notice that the ball bounces just like a light ray reflects off a mirror that is if the incoming velocity V makes an angle theta with the floor and the outgoing velocity called V prime makes the same angle to compute V Prime from V let's write V as the sum of two vectors a velocity parallel to the floor the parallel and the velocity perpendicular to the floor V perpendicular the only force during the collision is perpendicular to the floor because the floor pushes up on the ball so the parallel component won't change and the perpendicular component as before will be reversed meaning that V prime is equal to V parallel minus V perpendicular adding elasticity into the mix we get this equation cool we can use the idea of writing the velocity as the sum of parallel and perpendicular components to study the case when two particles I and J of the same mass collide let's draw a picture to make this clear the line I J from the center of particle I to the center of article J plays the role of the perpendicular to the floor so we write VI as a sum of two vectors as shown here we can do the same for VJ the only force acting on the particles during the collision is along the line IJ as before since no force is acting in the parallel direction the velocities in the parallel directions won't change to figure out exactly what happens in the perpendicular Direction requires using more advanced topics namely conservation of energy and momentum if we apply those concepts and assume that the particles have the same mass we find that particle i gets J's perpendicular velocity and vice-versa that is they swap perpendicular velocities that means after the collision the velocities V Prime I and V prime J are given by these equations that's it for particle collisions in the next exercise you'll have a chance to review these equations which describe collisions