Question

a piece of clay with mass m is traveling with an unknown velocity in the positive x-direction, when it collides and sticks to a block of mass 3m, moving with velocity v=-3m/s. after the collision, the block and clay are stuck together and traveling with a velocity of 1 m/s in the negative x-direction. what was the original velocity of the clay mass?

Answer 1

`5\ \text{m/s}`

Step-by-step explanation:

`m_1` = Mass of clay = m

`m_2` = Mass of block = 3m

`u` = Velocity of clay

`v` = Velocity of block = -3 m/s

`v_c` = Velocity of combined mass = -1 m/s

As mometum in the system is conserved we get

`m_1u+m_2v=(m_1+m_2)v_c\\\Rightarrow u=((m_1+m_2)v_c-m_2v)/(m_1)\\\Rightarrow u=((m+3m)* -1-3m* -3)/(m)\\\Rightarrow u=(5m)/(5)\\\Rightarrow u=5\ \text{m/s}`

The original velocity of the clay mass was
`5\ \text{m/s}`.