There are multiple explanations I can give for this, but let me start with the simplest one.
James Cameron wanted Jack to die - in fact, it was essential for the success of the movie that Jack dies in the end. You see, happy endings don't really sell well; so, Jack had to die for James to win all those Oscars he received for the movie.
Secondly, I think James Cameron is a perfectionist of perfectionists, and he would have thought of this problem too; he isn't stupid after all, and the most relevant explanation I am sure he could have come up is given by physics: and it's called Buoyancy. It's not about how much room there is on the plank, it's about how much weight it can take.
Buoyancy is an upward force exerted by a fluid, that opposes the weight of an immersed object.
Now, Buoyant Force = Volume of fluid Displaced x Gravitational Acceleration x Density of the Fluid
In layman terms, if buoyant force exerted by the fluid on you is equal to the force you exert on the fluid - which is basically your weight (mass * gravitational acceleration) - then, you float; else you sink.
Let's go over it once more :
Buoyant force = weight => float, good.
Buoyant force < weight => sink, bad.
As depicted in the picture, the length of the plank exceeds Kate Winslet's by, say, half a meter, Wikipedia tells me that Kate Winslet stands tall at 169 cm ( ); add to that another 50 cm and round it off to about 220 cm or 2.2 m. Breadth of the plank can be assumed to be a meter (give or take a few cm); a standard door as I can see from the measurements of my door is about 5 cm thick. Since it is the Titanic we are talking about here, I'll add a couple of cms to that thickness.
So as we have it:
Volume of water displaced by the plank(assuming it is fully submerged) = the volume of the plank = 2.2 x 1 x .07 = 0.154 m³.
Density of ocean water(salt water) = 1020 Kg/m³ ()
Gravitational acceleration = 9.8 m/s2
=> Buoyant force = 2.2 x 1 x .07 x 9.8 x 1020 = 1539.384 ~ 1540 N
now they will float if the total force exerted by the three bodies(Jack, Rose, and the door/plank) is less than this buoyant force.
Force exerted by the plank(weight) = Density of the plank(wood) x Gravitational acceleration x Volume of the plank
*density of wood = 650 Kg/m³ ()
=> Force exerted by the plank(weight) = 650 x 9.8 x 0.154 = 980.89 ~ 980 N
=> 1540 - 980 = 560 N
Now, 560/9.8 = 57.142 Kg
This means that in addition to its own weight, the plank could only support another 57.142 Kg and I am fairly certain that Rose must have at least weighed 45-50 Kg - she was a healthy girl after all, if you know what I mean.
So there you have it, it's not about the room on the plank, its about how much weight it could support. Think physics, people.More questions on Movie Story and Plot Themes: