Question

two masses, m1 and m2, are moving with velocities and when they collide. after the collision, the final velocities are and. which of the following expressions is true? (the subscripts x and y represent the components along x and y respectively.)

Answer 1

The only expression that is true is m

1

​

v

1x

​

+m

2

​

v

2x

​

=m

1

​

v

1x

′

​

+m

2

​

v

2x

′

​

. This is because the total momentum of the system must be conserved in a collision. The total momentum of the system is the sum of the momenta of the individual objects. In this case, the total momentum of the system is m

1

​

v

1x

​

+m

2

​

v

2x

​

before the collision and m

1

​

v

1x

′

​

+m

2

​

v

2x

′

​

after the collision. Since the total momentum of the system must be conserved, we have the following equation:

m

1

​

v

1x

​

+m

2

​

v

2x

​

=m

1

​

v

1x

′

​

+m

2

​

v

2x

′

​

The other expressions are not true because they do not conserve momentum. For example, the expression m

1

​

v

1y

​

+m

2

​

v

2y

​

=m

1

​

v

1y

′

​

+m

2

​

v

2y

′

​

is not true because it does not account for the momentum in the x-direction. The expression m

1

​

v

1x

​

=m

1

​

v

1x

′

​

is also not true because it does not account for the momentum of the second object.

Step-by-step explanation: