Question

An explosion blows a rock into three parts. two parts go off at right angles to each other. these two are, 1 kg first part moving with velocity 12 ms–1 and 2 kg, second part moving with velocity of 8 ms–1. if the third part flies off with a velocity of 4 ms–1, 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 θ with respect to -ve X direction (ie (90−θ) wrt to –ve Y-direction)
 
From Conservation of Momentum in X-Direction
m×4cosθ=2×8    −−−−−(1)
From Conservation of Momentum in Y-Direction
m×4sinθ=1×12   −−−−(2)
Dividing equation (2) wrt  (1), we get
tanθ=34⇒sinθ=35
Putting the value of sinθ in eq (2) we get
m=124sinθ=5
Therefore, mass of the third block is 5 Kg.

Answer 2

1st make a graph in xy plane and let 4ms^-1 be the resultant of 2 and 1 kg mass. Find the resultant it will be like

√ (1×12^2) + (2×8^2) = 20 this is momentum

Now we know that Momentum = m ×v

So 20=4× m

Hence M= 5kg