In a game of pool, the cue ball strikes another ball of the...

In a game of pool, the cue ball strikes another ball of the same mass and initially at rest. After the collision, the cue ball moves at 3.50 $\mathrm{m} / \mathrm{s}$ along a line making an angle of $22.0^{\circ}$ with the cue ball's original direction of motion, and the second ball has a speed of 2.00 $\mathrm{m} / \mathrm{s}$ . Find (a) the angle between the direction of motion of the second ball and the original direction of motion of the cue ball and (b) the original speed of the cue ball. (c) Is kinetic energy (of the centers of mass, don't consider the rotation) conserved?

Transcript

00:01 Alright so these are two balls here, right.

00:03 Then after collision we expect that we have this sort of the angle of deviation, you know, 22 degrees, is it? so therefore we expect that the first ball here will go there and the second ball will go that direction, right, after collision.

00:25 So that is what we visualize here.

00:29 So because we have initial velocity and final velocities of the cue ball, you know, before and after collision, so i'm going to have to say vi to be initial velocity of the cue ball, vf to be the final velocity, v2 to be the velocity of the other ball, okay.

00:50 And we have two angles here, you know.

00:53 If you split these two, you'll have tether 1 and tether 2, alright.

01:00 Tether 1 will be the angle between the original direction of the cue ball and the first deflection of the cue ball, right.

01:12 And so will be the second, the angle, that is the angle between the original direction of the cue ball, right, and the second deflected ball here.

01:26 So therefore in this case we're looking at mvf cos of tether 1 and here will be mvf m2 cos of tether 2, correct, so that at this particular plane we'll have mv2 sin of tether 2, correct.

01:58 And we'll have the same here but now we take tether 1 on the other side.

02:06 So in other words, we're trying to say that vf, or velocity final, is given as 3 .5 meters per second and tether 1 is given as 22 degrees, v2 is given as 2 meters per second, right.

02:29 So if we look at the x -axis for this, right, we expect that the conservation of momentum will be mvi proportional to mvf cos of tether 1, right, plus mv2 cos of tether 2, correct.

02:54 That is x.

02:56 Now let's, if you look at the y, you're looking at 0, right, minus sin of tether 1 plus mv2 sin of tether 2, correct.

03:13 So in other words, it's a very interesting calculation here.

03:20 So let's solve it and we discover that sin tether 2 will be equal to vf divided by v2, correct, multiplied by sin of tether.

03:29 So therefore, sin tether is 3 .5 divided by 2, sin of 22, correct...

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