Question

Two clouds collide and form another, more massive cloud. One cloud is stationary, while the other is traveling at 1 m/s. After the collision, the new, combined cloud travels with a velocity of 0.25 m/s. What is the ratio of the masses of the two original clouds

Answer 1

Answer: 3

Step-by-step explanation:

Given

One cloud is traveling at rate of
`u_2=1\ m/s`

combined velocity of the two is
`v=0.25\ m/s`

Suppose the masses of the clouds be
`m_1,m_2`

Conserving momentum

`\Rightarrow m_1u_1+m_2u_2=\left(m_1+m_2\right)v\\\text{Divide whole equation by }m_2\\\Rightarrow (m_1)/(m_2)u_1+u_2=\left((m_1)/(m_2)+1\right)v\\\\\Rightarrow 0+1=0.25(m_1)/(m_2)+0.25\\\\\Rightarrow (m_1)/(m_2)=(0.75)/(0.25)\\\\\Rightarrow (m_1)/(m_2)=3`