Question

Suppose two cars are headed toward each other. One is headed north with a mass of1,415 kg at a velocity of 22.9 m/s. The other is headed south with a mass of 819 kg at avelocity 11 m/s. They collide and stick together.What is their total velocity after the collision in the northern direction?

Answer 1

The initial momentum of the system is,

`p_i=m_1u_1+m_2u_2`

The final momentum of the system is,

`p_f=(m_1+m_2)v`

According to conservation of momentum,

`p_i=p_f`

Plug in the known expressions,

`\begin{gathered} m_1u_1+m_2u_2=(m_1+m_{2_{}})v \\ v=(m_1u_1+m_2u_2)/(m_1+m_2) \end{gathered}`

Substitute the known values,

`\begin{gathered} v=\frac{(1415\text{ kg)(22.9 m/s)+(819 kg)(11 m/s)}}{(1415\text{ kg+819 kg)}} \\ =\frac{32403.5\text{ kgm/s+}9009\text{ kgm/s}}{2234\text{ kg}} \\ =\frac{41412.5\text{ kgm/s}}{2234\text{ kg}} \\ \approx18.5\text{ m/s} \end{gathered}`

Therefore, the total velocity after the collision is 18.5 m/s