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 (-47 m/s) and a second piece, also of mass m, moves with velocity (-47 m/s) . 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?

a) 22.06m/s

b)45°

Explanation:

Let 'm' be  mass of 1st and 2nd pieces

mass of 3rd piece=3m

=velocity of 1st piece = -47iˆ  m/s

=velocity of 2nd piece = -47jˆ  m/s

=velocity of 3rd piece=?

By considering conservation of linear momentum, we have

m + m + 3m=0

+ + 3=0

3= - ( + )

= - ( + )

Substituting the values of and in above equation

= - (-47iˆ -47jˆ ) => 15.6iˆ + 15.6jˆ

(a)Magnitude of the velocity of  the third piece is given by

|| =√15.6²+15.6² => 22.06m/s

(b) its direction (as an angle relative to the +x axis)  'θ'

θ= => =>45°

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