A body A of mass m = 0.1 k g has an initial velocity of 3 i ^ m s - 1 . It collides elastically with another body B of the same mass which has an initial velocity of 5 j ^ m s - 1 . After the collisio

Question

A body A of mass m = 0.1 k g has an initial velocity of 3 i ^ m s - 1 . It collides elastically with another body B of the same mass which has an initial velocity of 5 j ^ m s - 1 . After the collision, A moves with a velocity v → = 4 i ^ + j ^ m s - 1 . The energy of B after the collision is written as x 10 J . The value of x is

TestHub · Accepted Answer

Using the principle of conservation of linear momentum

$0.1 \times 3 \hat{i} + 0.1 \times 5 \hat{j} = 0.1 \times 4 (\hat{i} + \hat{j}) + 0.1 \times \vec{v}$

$\vec{v} = (- \hat{i} + \hat{j}) m s^{- 1}$

$v = |\vec{v}| = \sqrt{2} m s^{- 1}$

$K_{B} = \frac{1}{2} \times 0.1 \times v^{2} = \frac{1}{10} J$

$x = 1$

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