Question

A body $A$ of mass $m=0.1 \, kg$ has an initial velocity of $3\hat{i} \, m \, s^{- 1}$ . It collides elastically with another body $B$ of the same mass which has an initial velocity of $5\hat{j} \, m \, s^{- 1}$ . After the collision, $A$ moves with a velocity $\overset{ \rightarrow }{v}=4\left(\hat{i} + \hat{j}\right)$ . The energy of $B$ after the collision is written as $\frac{x}{10} \, J$ . The value of $x$ is

Answer 1

Using the principle of conservation of linear momentum
$0.1\times 3\hat{i}+0.1\times 5\hat{j}=0.1\times 4\left(\hat{i} + \hat{j}\right)+0.1\times \overset{ \rightarrow }{v}$
$\overset{ \rightarrow }{v}=-\hat{i}+\hat{j}$
$K_{B}=\frac{1}{2}\times 0.1\times v^{2}=\frac{1}{10}J$
$x=1$