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 (-23 m/s) and a second piece, also of mass m, moves with velocity (-23 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

Explanation:

a. Given that:

mass of first & second piece, mass of 3rd piece,-velocity of first piece() and as velocity of 2nd piece ()

Let be velocity of 3rd piece=?

#Vessel is at rest before explosion. Considering conservation of linear momentum:

  #Dividing both sides by

#Plug the  values:

#So the magnitude of the third piece is:

Magnitude of the 3rd piece is 10.84 m/s

b. To find direction of the magnitude (as an angle relative to the -axis), we find . The angle is obtained by getting the tan inverse as:

-The direction of the magnitude (angle relative to the x-axis) is 45°