Question:
A body $A$, of mass $m=0.1 \mathrm{~kg}$ has an initial velocity of $3 \hat{i} \mathrm{~ms}^{-1}$. It collides elastically with another body, $B$ of the same mass which has an initial velocity of $5 \hat{j} \mathrm{~ms}^{-1}$. After collision, $A$ moves with a velocity $\vec{v}=4(\hat{i}+\hat{j})$. The energy of $B$ after collision is written as $\frac{x}{10} J$. The value of $x$ is
Solution:
(1) For elastic collision $K E_{\mathrm{i}}=K E_{f}$
$\frac{1}{2} m \times 25+\frac{1}{2} \times m \times 9=\frac{1}{2} m \times 32+\frac{1}{2} m v_{B}^{2}$
$34=32+V_{B}^{2} \Rightarrow V_{B}=\sqrt{2}$
$K E_{B}=\frac{1}{2} m v_{B}^{2}=\frac{1}{2} \times 0.1 \times 2=0.1 J=\frac{1}{10} J$
$\therefore x=1$