Acue ball traveling at 0.80 m/s hits the stationary 8-ball, which moves off with a speed of 0.27 m/s at an angle of 38° relative to the cue ball's initial direction. assuming that the balls have equal masses and the collision is inelastic, what will be the speed of the cue ball?

The speed of the cue ball is 0.2170 m/s

Explanation:

We can resolve this problem using conservation of linear momentum.

Calling the unit vector pointing in the initial direction of the cue ball, we get that the initial momentum is

As the 8 ball starts at rest, this means that

and, calling m the masses of both balls

Now, as there are no external forces in the horizontal direction, we know that the linear momentum is conserved. Calling the unit vector at 90° from and pointing at 52° from the 8-ball movement, we get:

The velocity of the cue ball will be

the momentum is

and this must be equal to the initial momentum

We get the equations

and

From the second equation, we get

putting this in the first equation

Now, using the equation

what was the acceleration of the 2 kg cart?

⇒ 16.0 cm/s2

what was the acceleration of the 4 kg cart?

⇒ 8.1 cm/s2

what was the acceleration of the 6 kg cart?

⇒ 5.3 cm/s2

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