After a head-on elastic collision between two | vedclass

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Question

(A) For a head-on elastic collision between two bodies of equal masses $(m_1 = m_2 = m)$,the bodies simply exchange their velocities.Let the initial v

Vedclass · Accepted Answer

$-2\,m/s$ and $+3\,m/s$

Vedclass · Answer

(A) For a head-on elastic collision between two bodies of equal masses $(m_1 = m_2 = m)$,the bodies simply exchange their velocities.Let the initial velocities be $u_1$ and $u_2$,and the final velocities be $v_1$ and $v_2$.According to the conservation of momentum: $m u_1 + m u_2 = m v_1 + m v_2$,which simplifies to $u_1 + u_2 = v_1 + v_2$.According to the property of elastic collision for equal masses: $v_1 = u_2$ and $v_2 = u_1$.Given the final velocities are $v_1 = +3\,m/s$ and $v_2 = -2\,m/s$.Therefore,the initial velocities must be $u_1 = v_2 = -2\,m/s$ and $u_2 = v_1 = +3\,m/s$.

After a head-on elastic collision between two balls of equal masses,one is observed to have a speed of $3\,m/s$ along the positive $x$-axis and the other has a speed of $2\,m/s$ along the negative $x$-axis. What were the original velocities of the balls?

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