Two balls collide head-on in an elastic collision. The first...

Two balls collide head-on in an elastic collision. The first ball has a mass of 3 kg and speed of 20 m/s in the negative x direction. The second ball has a mass of 2 kg and a speed of 30 m/s in the positive x direction. 30 m/s before 20 m/s 2 kg 3 kg v'2 after v'1 2 kg 3 kg What is the relative velocity "v'2 - v'1" of the two balls after the collision (use sign to indicate the direction, with left-to-right as the positive direction)? Answer in units of m/s.

Transcript

00:02 Dear student, so the elastic collision for the final values of the elastic collision for the body 1 is let's say there is v1, this is the final velocity of the body 1.

00:16 So this equals the difference of the masses m1 minus m2 divided by the sum of the masses there is m1 plus m2 times the initial velocity of the body 1.

00:31 Let's say there is u1 plus twice of the body two twice of the mass of the body two divided by sum of both masses times the velocity of the initial velocity of the second body so maria student let's plug in the values mass one is two kilogram mass two is three kilograms divided by two plus three kilograms the initial velocity of the body one is 30 meters per second plus twice of the mass of the second body is 3 kilograms divided by their sum is 2 plus 3 kilograms times the initial velocity of the body 2 is minus 20 meters per second because this is in opposite direction so from here the final velocity of the body 1 that is v1 so this equals negative 30 meters per second because this is in opposite direction likewise the final velocity of the body 2 is denoted with v2.

01:32 So the formula for the formula for the final velocity of the body 2 would be twice of the mass of the body 1 divided by some of the masses of the both bodies there is m1 plus m2 plus sorry times the initial velocity of the body 1 plus the difference of the masses of both bodies there is m2 minus m1 divided by their sum there is m2 plus m1 times the initial velocity of the body 2 that is u 2 now let's plug in the values dear student we have been given all the masses 2 into mass of the body 1 is 2 kilograms initial velocity of the body 1 is 30 meters per second so the sum of the bodies is 2 plus 3 2 is the mass of the body 1 3 kilograms is the mass of the body 2 times the difference of the masses is 3 minus 2 kilograms divided by their sum is 2 plus 3 kilograms the initial velocity of the body 1 is negative 20 meters per second so from here the final velocity of the body 2 that is v2 so this equals 20 meters per second now my dear student the relative velocity of both bodies let's denote that with we are so this is the difference of the final velocities of the both bodies, that is v2 minus v1.

03:03 So let's plug in the values because both the bodies are moving in the opposite direction.

03:11 V2 is 20 meters per second.

03:13 V1 was negative 30 meters per second...

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