an object explode and a to 2 kilograms piece moves north at 4 m/s and a 4 kilograms piece moves East at 1.5 meters per second. What is the momentum of the third piece? What is the mass of the third piece if it moves at a speed of 4 meters per second?

To calculate momentum, you multiply the mass of an object by its velocity. In this case, we have two separate pieces moving in different directions. Let's calculate the momentum of each piece individually and then determine the momentum of the third piece.

The momentum (p1) of the first piece, weighing 2 kilograms, moving north at 4 m/s, can be calculated as follows:
p1 = (mass1) x (velocity1)
p1 = (2 kg) x (4 m/s)
p1 = 8 kg·m/s

The momentum (p2) of the second piece, weighing 4 kilograms, moving east at 1.5 m/s, can be calculated as follows:
p2 = (mass2) x (velocity2)
p2 = (4 kg) x (1.5 m/s)
p2 = 6 kg·m/s

To determine the momentum of the third piece, we need to consider the conservation of momentum in an explosive event. In this case, we know that the initial momentum of the system is equal to the final momentum:

Initial momentum = Final momentum

Considering the direction of the two pieces, we can resolve their momenta into x (east) and y (north) components:

Initial momentum in the x-direction = p2 (since p1 is only in the y-direction)
Final momentum in the x-direction = p3 (momentum of the third piece)

Now we can use these components to calculate p3:

p2 (x-component) = p3
6 kg·m/s = p3

So the momentum of the third piece is 6 kg·m/s.

To determine the mass of the third piece if it moves at a speed of 4 m/s, we can rearrange the momentum equation:

Momentum (p) = mass (m) x velocity (v)

Rearranging the formula to solve for mass (m):

mass (m) = momentum (p) / velocity (v)

Substituting the known values:

mass (m) = 6 kg·m/s / 4 m/s
mass (m) = 1.5 kg

Therefore, the mass of the third piece moving at a speed of 4 m/s would be 1.5 kilograms.