Question

An explosion blows a rock into three parts two parts go off at right angels to each other these two are 1 kg first part moving with a velocity

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.