An exploision blows a rock into 3parts. two go off at right angles to each other. These 2 are, 1kg first part with velocity 12m/s and 2kg second part with velocity of 8m/s. If the third part flies off with a velocity of 4m/s, its mass would be
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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.
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.
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