Question

Imagine an asteroid at rest in space that cracks into two pieces. The first piece moves at 1.4 times the speed of the second piece. Calculate the ratio of the first piece’s mass to the second piece’s mass

Answer 1

Since the total linear momentum of the system was 0 before the asteroid cracking into two pieces, then the magntude of the linear momentum of each piece must be the same after the cracking.

Then:

`m_1v_1=m_2v_2`

If the speed of the first piece is 1.4 times the speed of the second, then:

`\begin{gathered} v_1=1.4v_2 \\ \Rightarrow m_1*1.4v_2=m_2v_2 \\ \Rightarrow1.4m_1=m_2 \\ \Rightarrow m_1=(m_2)/(1.4) \\ \Rightarrow(m_1)/(m_2)=(1)/(1.4) \end{gathered}`

Then, the ratio of the first piece's mass to the second piece's mass is 1:1.4