Two friends are standing on opposite ends of a canoe that is initially at rest with respect to a frictionless lake. the person in the front throws a very massive ball toward the back, and the person in the back catches it. after the ball is caught the canoe is

Here we can say that the momentum of the system will remain conserved

As here we can see that there is no external force in horizontal direction

so here we can say that

As the person in front throw the ball towards back the canoe will start moving forward direction so that momentum of the system will remain conserved

now after this we can say momentum of ball + canoe + two friends = 0 always

now when the person at the back of the canoe will catch the ball then again due to the concept of momentum conservation we can say that the whole system will again comes to rest

so the canoe will become at rest after the person at the back will catch the ball

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)

answer is slate

hope this