A 0.16 kg billiard ball moving at 1.20 m/s collides elastically with one of the same mass

at rest. It continues at a speed of 0.6 m/s afterward in a different direction from before.
What is the final speed of the other billiard ball?
I thought it was 0.6 m/s but it says I am wrong.

To find the final speed of the other billiard ball after the collision, we can use the principle of conservation of linear momentum.

The principle of conservation of linear momentum states that the total linear momentum of an isolated system remains constant before and after a collision. In an elastic collision, both the total linear momentum and total kinetic energy of the system are conserved.

The linear momentum (p) of an object is defined as the product of its mass (m) and velocity (v), so we can write the equation:

p1i + p2i = p1f + p2f

where:
p1i = initial momentum of the first billiard ball
p2i = initial momentum of the second billiard ball
p1f = final momentum of the first billiard ball
p2f = final momentum of the second billiard ball

Since the first billiard ball is moving at 1.20 m/s and collides elastically with the second ball at rest, its initial momentum is:

p1i = m1 * v1i
p1i = (0.16 kg) * (1.20 m/s)
p1i = 0.192 kg·m/s

The second billiard ball is at rest initially, so its initial momentum is:

p2i = m2 * v2i
p2i = (0.16 kg) * (0 m/s)
p2i = 0 kg·m/s

After the collision, the first ball continues at a speed of 0.6 m/s, but in a different direction. The final momentum of the first ball is:

p1f = m1 * v1f
p1f = (0.16 kg) * (-0.6 m/s) [Note: We take the negative sign since the direction is reversed]
p1f = -0.096 kg·m/s

Now, we can use the conservation of momentum equation to find the final momentum of the second ball:

0.192 kg·m/s + 0 kg·m/s = -0.096 kg·m/s + p2f

Simplifying the equation, we have:

0.192 kg·m/s = p2f - 0.096 kg·m/s
p2f = 0.192 kg·m/s + 0.096 kg·m/s
p2f = 0.288 kg·m/s

Finally, we can find the final speed of the second ball by dividing the final momentum by its mass:

v2f = p2f / m2
v2f = (0.288 kg·m/s) / (0.16 kg)
v2f = 1.8 m/s

Therefore, the final speed of the other billiard ball after the collision is 1.8 m/s.

To determine the final speed of the other billiard ball, we can use the principle of conservation of linear momentum. In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.

Let's denote the initial velocity of the first billiard ball as v1_initial, the initial velocity of the second billiard ball as v2_initial, the final velocity of the first ball as v1_final, and the final velocity of the second ball as v2_final.

According to the problem, the first billiard ball has a mass of 0.16 kg and is initially moving at a velocity of 1.20 m/s. The second billiard ball has the same mass and is initially at rest.

Using the conservation of linear momentum, we can write the equation:

(m1 * v1_initial) + (m2 * v2_initial) = (m1 * v1_final) + (m2 * v2_final)

Substituting the given values:

(0.16 kg * 1.20 m/s) + (0.16 kg * 0 m/s) = (0.16 kg * v1_final) + (0.16 kg * v2_final)

0.192 kg*m/s = 0.16 kg * v1_final + 0.16 kg * v2_final

Since we know that the final velocity of the first billiard ball is 0.6 m/s, we can substitute this value into the equation:

0.192 kg*m/s = 0.16 kg * 0.6 m/s + 0.16 kg * v2_final

0.192 kg*m/s - 0.16 kg * 0.6 m/s = 0.16 kg * v2_final

0.192 kg*m/s - 0.096 kg*m/s = 0.16 kg * v2_final

0.096 kg*m/s = 0.16 kg * v2_final

Now we can solve for v2_final:

v2_final = (0.096 kg*m/s) / 0.16 kg

v2_final = 0.6 m/s

Therefore, the final velocity of the other billiard ball is indeed 0.6 m/s.

M1*V1 + M2*V2 = M1*V3 + M2*V4.

0.16*1.2 + 0.16*0 = 0.16*0.6 + 0.16*V4. V4 = ?.