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Question
A block at rest explodes into three equal parts. Two parts start moving along X and Y axes respectively with equal speeds of 10 m/s. Find the initial velocity of the third part.
Solution
As the block is exploded only because of its internal energy, the net external force on the system is zero.
Thus, the centre of mass of does not change.
Let the body was at the origin of the co-ordinate system during explosion.
Resultant velocity of two bodies of equal mass moving at a speed of 10 m/s in + x-axis and + y-axis direction, is given as:
\[v = \sqrt{{10}^2 + {10}^2 + 2 . 10 . 10 \cos 90^\circ \ } = 10\sqrt{2}\text{ m/s,} 45^\circ \text{ w . r . t x - axis }\]
If the centre of mass is at rest, the third part having equal mass as that of the other two masses will move in the opposite direction (i.e.\[135^\circ\] w.r.t. +x-axis) at the same velocity of \[10\sqrt{2} \text{ m/s } .\]
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