Question

an explosion blows a rock into three parts. two parts go off right angle to each other these two are, 1kg first moveing with velocity 12 m/s and 2 kg, second part moving with velocity of 8 m/s. if the third part flies off with a velocity of 4 m/s, its mass would be

Answer 1

Suppose mass of 1kg start moving in positive +ve Y-direction and of mass 2 kg in positive +ve X-direction (Since both making right angle to each other).
Let the mass of the third block be m Kg and its start moving towards the direction making an angle $\theta$ with respect to -ve X direction (ie $(90-\theta )$ wrt to –ve Y-direction)

From Conservation of Momentum in X-Direction
$m\times 4\cos \theta =2\times 8-----\left(1\right)$
From Conservation of Momentum in Y-Direction
$m\times 4\sin \theta =1\times 12----\left(2\right)$
Dividing equation (2) wrt (1), we get
$\tan \theta =\frac{3}{4}\Rightarrow \sin \theta =\frac{3}{5}$
Putting the value of $sin\theta$ in eq (2) we get
$m=\frac{12}{4\sin \theta }=5$
Therefore, mass of the third block is 5 Kg.