A $5000kg$open train car is rolling on frictionless rails at $22m/s$when it starts pouring rain. A few minutes later, the car’s speed is $20m/s$. What mass of water has collected in the car?

We need to find the mass of water that collected in the car.

Because of isolated system the railway is frictionless. The object has mass $m$and moves with speed $v$that has momentum $p$, Vector is a product of object's mass and its velocity.The momentum is given by equation in the form

role="math" localid="1649868600557" $p=mv$

Using expression $p$into equation $\left(1\right)$

$m_f{v}_f=m_i{v}_i\left(2\right)$

$m_i=5000kg$is the mass of train before raining and it becomes $m_f$ after raining. Putting values for $m_i,v_{i}and{v}_{f}toget{m}_f$We have to solve equation $\left(2\right)$for $m_f$

$$\begin{gathered} m_f=\frac{m_i{v}_i}{v_f} \\ =\frac{\left(5000kg\right)\left(22m/s\right)}{\left(20m/s\right)} \\ =5500kg \end{gathered}$$

To get mass of the water in the car by

$$\begin{gathered} m_{water}=m_f-m_i \\ =5500kg-5000kg \\ =500kg \end{gathered}$$