1. The problem statement, all variables and given/known data A friend asking: A cart and a water hose: A water hose is spraying water at rate m_dot kg/sec, and at a given velocity V, on a cart with a mass M. The water hit the cart, and they are bounced back from it in an elastic collision (same velocity in relation to the cart, but opposite direction). What is the velocity of the cart as a function of time, v(t)? 2. Relevant equations 3. The attempt at a solution "My way of solution was this: Lets have a coordinate system that moves with the same velocity with the cart at a certain time. Delta_m would signify the small amount of water. Then we write the momentum at time t, and t+dt: P(t)=Delta_m*(V-v(t)) P(t+dt)=Delta_m*(v(t)-V)+M*dv P(t)=P(t+dt), so: dv/(V-v(t)) = (2*Delta_m/M) Delta_m = m_dot*dt, so: dv/(V-v(t))=2m_dot*dt/M --> ln(V-v(t))=-2m_dot*t/M + C, and then we can get v(t) by using exp. However, the final answer I've seen is v(t) = (2m_dot*t/M)/(1+2m_dot*t/M), Which is obviously not an end result of an exp/ln function. What is wrong with my solution? How do I arrive at the right solution?"