A42-g firecracker is at rest at the origin when it explodes into three pieces. the first, with mass 12 g, moves along the x-axis at 35 m/s. the second, with mass 21 g, moves along the y-axis at 29 m/s. find the velocity of the third piece.

u₃  = - 46.66 i  -67.66 j

Explanation:

Given that

M= 42 g

Initial speed ,u= 0 m/s

m₁ = 12 g ,u₁=35 i m/s

m₂=21 g,u₂=29 j m/s

Lets take mass of the third mass = m₃

The speed of the third mass = u₃ m/s

From mass conservation

M= m₁+ m₂ +  m₃

42 = 12 + 21 +  m₃

m₃= 9 g

There is no any external force that is why linear momentum will be conserve

M u = m₁ u₁+m₂u₂+m₃u₃

42 x 0 = 35 i x 12 + 21 j x 29 + 9  u₃

9 u₃  = -420 i - 609 j

u₃  = -46.66 i  -67.66 j

Therefore the speed of the third block will be

u₃  = - 46.66 i  -67.66 j

grav potential energy

r = ρ x length / area  

ρ = r x area / length  

ρ is in ohm-meters  

in basic units, it is m³kg/s³a²  

i think this is it.