As you can imagine, the left movement of the ship has two effects on the rope: one is to make the rope "move left" and the other is to make the end of the rope turn clockwise. These two movements have corresponding speeds, in which the speed of moving the rope to the left should be equal to the speed of pulling the rope to the left, so that the rope can be straightened ... so v0 = vCOSθ in other words, v=v0/cosθ.
Acceleration is caused by force, so it is the tension of the rope that causes the acceleration of the ship. The vertical tension of the rope balances gravity with buoyancy, so the horizontal separation of rope tension brings the acceleration of the ship moving to the left. Man and rope can be regarded as a whole, so the acceleration is the same, both a0. So a=a0*cosθ.
If you really can't figure it out, it will be much faster without the limit method mentioned upstairs. But I still suggest that you can figure out the decomposition problem so that it can be applied everywhere. ..