How Fast Must a Camper Slide to Reach the Shore by Throwing Rocks?

[soto2018]

Homework Statement

An adventurous camper (71 kg) finds him/her self stranded in the middle of a frozen lake (diameter = 1.3 km) with only a bag of rocks (total mass 10.0 kg). The ice is so slippery, that they move about the lake's surface without friction (don't ask me how they got there in the first place). Remembering what they learned in a physics lab, they devise a way to get themselves to the edge of the lake by throwing the bag of rocks in the opposite direction of the shore with a velocity of 6.0 m/s. If they throw the rocks all at once, how long does it take for them to slide to shore?

Homework Equations

The topic of the lab was elastic and inelastic collisions, however this problem doesn't really have to do with the other questions.
Sum of Fx=ma

The Attempt at a Solution

Since it's on a friction-less surface, I know that the sum of the forces in the x direction is equal to ma, and that the velocity is what causes the camper and his rocks to keep moving, however I don't know where to go from there. I've tried using some of the kinematics formulas to try to solve for t, but I can't seem to get it right.

 

[ehild]

Homework Statement

An adventurous camper (71 kg) finds him/her self stranded in the middle of a frozen lake (diameter = 1.3 km) with only a bag of rocks (total mass 10.0 kg). The ice is so slippery, that they move about the lake's surface without friction (don't ask me how they got there in the first place). Remembering what they learned in a physics lab, they devise a way to get themselves to the edge of the lake by throwing the bag of rocks in the opposite direction of the shore with a velocity of 6.0 m/s. If they throw the rocks all at once, how long does it take for them to slide to shore?

Homework Equations

The topic of the lab was elastic and inelastic collisions, however this problem doesn't really have to do with the other questions.

Welcome to PF!

If you reverse time it is the usual inelastic collision. :D

When the man throws the bag of ball, he exerts F force at the bag and the bag exerts F force at the man in the opposite direction. There is no external force, so the change of the total momentum of the system man + bag is zero.
During their interaction, the acceleration of bag is a_bag=F/m_bag and the acceleration of the man is a_man=-F/m_man. The man exerts force on the bag for a very short Δt time. Assuming constant F the velocity of the bag is V_bag=F/m_bag Δt and the velocity of the man is Vman=-F/m_man Δt , that is V_man m_man + V_bag m_bag=0. You know the masses and the velocity of the bag. What is the velocity of the man?