- #1

utkarshakash

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## Homework Statement

A shell flying with velocity v = 500 m/s bursts into three identical fragments so that the kinetic energy of the system increases η = 1.5 times. What maximum velocity can one of the fragments obtain?

## Homework Equations

Conservation of Momentum

Conservation of Energy

## The Attempt at a Solution

[itex]K.E._{initial}=\frac{1}{2} mv^{2}[/itex]

Let final velocities be [itex]v_{1}, v_{2} and v_{3}[/itex]

[itex]K.E._{final}=\frac{1}{2} \left[ \frac{m}{3} v_{1}^{2}+ \frac{m}{3} v_{2}^{2}+ \frac{m}{3} v_{3}^{2}\right] [/itex]

From question

[itex] K.E._{final}= η K.E._{initial} [/itex]

Putting the values of K.E. I get a relation

[itex]=3v^{2}η = v_{1}^{2}+ v_{2}^{2}+ v_{3}^{2}[/itex]

Also using conservation of momentum

[itex]mv = \frac{m}{3}\left(v_{1}+v_{2}+v_{3}\right)[/itex]

which simplifies to

[itex] 3v = (v_{1}+v_{2}+v_{3}) [/itex]

But now I'm stuck here. What to do next to find the maximum velocity?