On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision, the first block moves at an angle θ to its initial direction and has a speed v/3/ The second block's speed after the collision is

$fraction numerator 2 square root of 2 over denominator 3 end fraction space v$

3/4 v

$fraction numerator 3 over denominator square root of 2 end fraction space straight v$
$fraction numerator square root of 3 over denominator 2 end fraction straight v$

Solution

fraction numerator 2 square root of 2 over denominator 3 end fraction space v

According to law of conservation of kinetic energy, we have

1 half Mv squared space plus 0 space equals space 1 half straight M open parentheses straight v over 3 close parentheses squared space plus space 1 half Mv subscript 2 superscript 2 rightwards double arrow space straight v squared space equals space straight v squared over 9 space plus straight v subscript 2 superscript 2 rightwards double arrow space straight v squared space minus fraction numerator straight v squared over denominator space 9 end fraction space equals space straight v subscript 2 superscript 2 space rightwards double arrow space fraction numerator 8 straight v squared over denominator 9 end fraction Velocity space of space second space block space after space collision space straight v subscript 2 space equals space fraction numerator 2 square root of 2 over denominator 3 end fraction straight v

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