Ii a ball of mass 0440 kg moving east chi direction with a...

(II) A ball of mass 0.440 kg moving east ( $+\chi$ direction) with a speed of 3.80 m/s collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?

Transcript

00:01 Hello everyone, here in this question there are two balls.

00:04 One with mass m1 given as 0 .44 kg and another with mass m2 is given as 0 .22 kg.

00:17 One with initial velocity u1 is given as 3 .8 meter per second while the velocity or initial velocity of the second ball is given as 0.

00:33 That is, it is at rest initially.

00:36 Now, suppose after collision, the velocity of m1 is v1 and m2 is v2, right? these are velocities after collision, right? after collision.

00:58 Now, this collision is elastic collision, right? so linear momentum, linear momentum and energy will be conserved right so first of all let us conserve the linear momentum right that is initial linear momentum must be equals to final linear momentum that implies we can write m1 u1 plus m2 u2 must be equals to m1 v1 plus m2 v2 right that implies as u 2 is 0 this term goes to 0 and will get m1 u1 must be equals to m1 v1 plus m2 v2 suppose this is equation 1 right now again the energy is also conserved that is initial energy must be equals to final energy that is we will we can write half m1 u1 square plus half m2 u2 square must be equals to half m1 v1 square plus half m2 v2 square right now again u2 is 0 so this term goes to 0 and we get m1 u1 u1 square as equals to m1 v1 square plus m2 v2 square right suppose this is equation 2 now by solving this equation 1 and equation 2 we will get v1 will be equals to u1 multiplied by m1 minus m 2 whole divided by m1 plus m2 and v2 will be equals to 2 m1 m1 u 1 whole divided by m 2 and v2 will be equals to 2 m1 u 1 whole by m1 plus m2, right? so v1 will be what? that implies putting values, we will get v1 will be equals to u1, that is 3 .8, multiplied by 0 .44 minus 0 .22, whole divided by m1 is 0 .44 plus 0 .22, right? now calculating this, we will get v2...

Question

(II) A ball of mass 0.440 kg moving east ( $+\chi$ direction) with a speed of 3.80 m/s collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?

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