Answer
The dog is $~~4.2~m~~$ from the shore.
Work Step by Step
As the dog moves, the position of the center of mass of the dog-boat system does not move relative to the shore.
Therefore, the as the dog moves toward the shore, the boat must move away from the shore a distance $d$ Then the dog's net displacement relative to the shore is $(2.4-d)$.
We can find the distance $d$ that the boat moves away from the shore:
$(18~kg)~d = (4.5~kg)(2.4-d)$
Note that the two sides of this equation must be equal since the position of the center of mass does not move.
We can find the distance that the boat moves away from the shore:
$(18)~d = (4.5)(2.4-d)$
$18~d = 10.8-4.5~d$
$22.5~d = 10.8$
$d = \frac{10.8}{22.5}$
$d = 0.5~m$
The dog's net displacement toward the shore is $(2.4~m-0.5~m)$ which is $1.9~m$
The dog's final distance from the shore is $(6.1~m-1.9~m)$ which is $4.2~m$
The dog is $~~4.2~m~~$ from the shore.
