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  4. A 5 kg shell kept at rest suddenly splits up into three parts. If two parts of mass 2 kg each are found flying due north and east with a velocity of 5 m / s each, what is the velocity of the third part after explosion?

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Q. A $5\, kg$ shell kept at rest suddenly splits up into three parts. If two parts of mass $2\, kg$ each are found flying due north and east with a velocity of $5\, m / s$ each, what is the velocity of the third part after explosion?

Laws of Motion

Solution:

image
$p_{x}=\text { momentum along east }=10 kg m / s $
$p_{y}=\text { momentum along north }=10\, kg\, m / s$
Resultant momentum,
$p=\sqrt{p_{x}^{2}+p_{y}^{2}}=\sqrt{10^{2}+10^{2}}=10 \sqrt{2} kg\, m / s$ due north-east
According to the law of conservation of momentum
$p+p_{3}=0 \,\,\,\,\text { or } \,\,\,\, p_{3}=-p \quad \text { or } \,\,\, p_{3}=-10 \sqrt{2} \,kg\, m / s$
or $ p_{3}=10 \sqrt{2} kg \,m / s$ due south-west
$\therefore v_{3}=\frac{p_{3}}{m_{3}}=\frac{10 \sqrt{2}}{1}=10\, \sqrt{2} m / s \text { due south-west } $