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

Answer:

$5\ \text{m/s}$

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

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

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