In the horizontal direction of the railroad car, the momentum will be conserved. Also, the final speed of the car is equal to the final speed of the snow.

Given data

The mass of the car is\(m = 4800\;{\rm{kg}}\).

The constant speed of the car is\(v = 7.60\;{\rm{m/s}}\).

The rate of fall is\(c = 3.80\;{\rm{kg/min}}\).

The time is\(t = 60\;{\rm{min}}\).

The relation from conservation of momentum is given by the following:

\(\begin{array}{c}P = P'\\mv = \left( {m + m'} \right)v'\\v' = \frac{{mv}}{{\left( {m + m'} \right)}}\end{array}\)

Here,\(m'\)is the mass of the snow, and\(v'\)is the speed of the car.

Plugging the values in the above equation,

\(\begin{array}{l}v' = \left[ {\frac{{\left( {4800\;{\rm{kg}}} \right)\left( {7.60\;{\rm{m/s}}} \right)}}{{\left( {4800\;{\rm{kg}} + 3.80\;{\rm{kg/min}} \times {\rm{60}}\,{\rm{min}}} \right)}}} \right]\\v' = 7.25\,{\rm{m/s}}\end{array}\)

Thus, \(v' = 7.25\,{\rm{m/s}}\) is the required number of rebounds made by the ball.