A vessel at rest at the origin of an xy coordinate system explodes into three pieces. Just after the explosion, one piece, of mass m, moves with velocity (-31 m/s) i and a second piece, also of mass m, moves with velocity (-31 m/s) j. The third piece has mass 3m. Just after the explosion, what are the (a) magnitude and (b) direction (as an angle relative to the + x axis) of the velocity of the third piece?

Question

Araceli Mercado

Physics

8 August, 09:10

A vessel at rest at the origin of an xy coordinate system explodes into three pieces. Just after the explosion, one piece, of mass m, moves with velocity (-31 m/s) i and a second piece, also of mass m, moves with velocity (-31 m/s) j. The third piece has mass 3m. Just after the explosion, what are the (a) magnitude and (b) direction (as an angle relative to the + x axis) of the velocity of the third piece?

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Guadalupe Lamb · Answer 1

The momentum of the first piece = m v = - m x 31 i kg m/s in - x direction direction

The momentum of the second piece = - m x 31 j kg m / s in Y - direction

Total momentum = - 31 m (i + j)

To conserve momentum, the third piece must have momentum equal to this

and opposite to it

So momentum of the third piece = 3m x V = 31 m (i + j)

V = 31/3 (i + j) =

Magnitude of velocity V = √2 x 31 / 3 = 14.6 m / s

Its direction will be towards the vector i + j ie 45° from x - axis in positive direction