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°

explanation:

earth's surface is mainly heated by the absorption of infrared radiation from the sun.

evaporation occurs because molecules in liquid water are warmed ( usually by the sun) and vibrate quicker, becoming less dense and rise.

condensation occurs because molecules in water vapor are cooled and therefore vibrate more slowly thus becoming more dense and eventually fall to earth.

lines of equal barometric pressure on a weather map are called: isobars : lines of equal temp on a weather map are called: isotherms.​