Question

An empty sled of mass M moves without friction across a frozen pond at speed v_o. Two objects are dropped vertically into the sled one at a time: first an object of mass m and then an object of mass 2m. Afterward the sled moves with speed v_f. What would be the final speed of the sled if the objects were dropped into it in reverse order? 

(A) v_f 

(B) v/3_f 

(C) v/2 

(D) 2v_f 

(E) 3v_f 

Answer 1

Correct option (c) v_f

Its does not matter what order to masses are dropped in. Adding mass reduces momentum proportionally. All that matters is the total mass that was added. This can be provided by finding the velocity after the first drop, then continuing to find the velocity after the second drop. Then repeating the problem in reverse to find the final velocity which will come out the same.