Question

A white pool ball of mass 1.0 kg moving at 10 m/s collides with
a 1.2 kg red pool ball initially at rest. After the collision, the
white pool ball continues in the same direction with a velocity
of 3.0 m/s. Neglecting friction, the velocity of the red ball after
the collision is __m/s. (Round to the nearest tenth).

Answer 1

The velocity of the red ball after the collision is 5.8 m/s

Explanation:

In absence of external forces on the system, we can apply the principle of conservation of momentum. The total momentum of the system must be conserved before and after the collision, so we can write:

$p_i = p_f\\m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$

where:

$m_1 = 1.0 kg$ is the mass of the pool ball

$u_1 = 10 m/s$ is the initial velocity of the pool ball

$v_1 = 3.0 m/s$ is the final velocity of the pool ball

$m_2 = 1.2 kg$ is the mass of the red ball

$u_2 = 0$ is the initial velocity of the red ball

$v_2$ is the final velocity of the red ball

Solving the equation for v2, we find the final velocity of the red ball after the collision:

$v_2 = \frac{m_1 u_1-m_1v_1}{m_2}=\frac{(1.0)(10)-(1.0)(3.0)}{1.2}=5.8 m/s$

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Answer 2

The final velocity of the red pool ball after the collision is 5.8 m/s.

How do you calculate the final velocity of the red pool ball?

The pool balls move in the absence of any external force. Hence the law of conversion of momentum is applicable on the balls. According to the law of conversion of momentum, the magnitude of the momentum of the balls before and after the collision will be the same.

Momentum Before Collision = Momentum After Collision

$m_1u_1 +m_2u_2 = m_1v_1 +m_2v_2$

Here m1 and m2 are the mass of the white and red pool ball. u1 and u2 are the initial velocities of the white and red pool ball before the collision. v1 and v2 are the final velocities of the white and red pool ball after the collision.

Given that $m_1 = 1\;\rm kg$, $m_2 = 1.2\;\rm kg$, $u_1 = 10 \;\rm m/s$, $u_2 = 0\;\rm m/s$ and $v_1 = 3\;\rm m/s$

Substituting the given values in the above equation, the final velocity of the red pool ball is,

$1\times 10 + 1.2\times 0 = 1\times 3 +1.2\times v_2$

$v_2 = \dfrac {10-3}{1.2}$

$v_2 = 5.8\;\rm m/s$

Hence we can conclude that the final velocity of the red pool ball after the collision is 5.8 m/s.

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https://brainly.com/question/9163788.