Question

Ball B, with a mass of 30kg, is moving to the left at -10 m/s. With what velocity should Ball A, with a mass of 10 kg, move to the right and collide with B, so that Ball A rebounds with a velocity of -30 m/s, and Ball B with velocity of 10 m/s, after the collision? Assume the collision to be perfectly elastic

Inelastic formula

Answer 1

Initial velocity of ball A is 30 m/s to the right

Explanation:

Here we can use the principle of conservation of momentum. In fact, the total momentum of the two-balls system must be conserved before and after the collision. Therefore, we can write:

$p_i = p_f\\m_A u_A + m_B u_B = m_A v_A + m_B v_B$

where:

$m_A = 10 kg$ is the mass of the first ball

$u_A$ is the initial velocity of the first ball

$v_A = -30 m/s$ is the final velocity of the first ball

$m_B = 30 kg$ is the mass of the second ball

$u_B = -10 m/s$ is the initial velocity of the second ball  (to the left)

$v_B = +10 m/s$ is the final velocity of the second ball

Re-arranging the equation and solving for $u_A$, we find the initial velocity of the first ball:

$u_A =\frac{m_A v_A + m_B v_B -m_B u_B}{m_A}=\frac{(10)(-30)+(30)(+10)-(30)(-10)}{10}=30 m/s$

And the positive sign means the initial direction is to the right.

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