The solution to a problem from "Introduction to Mechanics" by Kleppner and Kolenkow has created a doubt in my head.
A sand-spraying locomotive sprays sand horizontally into a freight car as shown in the sketch below. The locomotive and freight car are not attached. The engineer in the locomotive maintains his speed so that the distance to the freight car is constant. The sand is transferred at a rate $b=10 kg/s$ with a velocity $u=5 m/s$ relative to the locomotive. The freight car starts from rest with an initial mass of $M_0= 2000 kgs$. Find its speed after $t=100 s$.
The solution to the problem 4.13 is on page 61. I am in a belief that the solution is not correct.
The solution considers the momentum of the system( defined in the solution ) to be conserved. The problem I find with the solution is, the sand( part of the system ) is being accelerated by the locomotive( as the locomotive keeps up with the speeding freight car ), suggesting the presence of an external force( exerted by the locomotive ) on the system. The solution clearly states that the external force on the system is zero. What am I not understanding here?