Answer:
a. The objects will collide and move forward in the direction that the first object was moving in.
Explanation:
Linear Momentum
The total linear momentum on an isolated system of particles is conserved regardless of their internal interactions. In a two-mass system, the total momentum is expressed as
[tex]p=m_1v_1+m_2v_2[/tex]
where m1, m2, v1, v2 are the object's masses and speeds respectively.
If one object is at rest and the other hits it inelastically, then part of the kinetic energy is converted into other forms and both objects remain together at a speed we can compute, knowing that the total momentum after the impact is
[tex]p'=m_1v_1'+m_2v_2'[/tex]
Equating p=p'
[tex]m_1v_1'+m_2v_2'=m_1v_1+m_2v_2[/tex]
Both masses remain at the same speed after the collision, so
[tex]v_2'=v_1'=v'[/tex]
Thus
[tex](m_1+m_2)v'=m_1v_1+m_2v_2[/tex]
Solving for v'
[tex]\displaystyle v'=\frac{m_1v_1+m_2v_2}{m_1+m_2}[/tex]
We know v2=0
[tex]\displaystyle v'=\frac{m_1}{m_1+m_2}v_1[/tex]
Note both objects will move at a fraction of the original speed and in the same direction. Thus, the correct answer is
a. The objects will collide and move forward in the direction that the first object was moving in.
