In this issue of Math in the News we analyze the sinking of the Titanic. It has been a hundred years, yet the story of the sinkin g of the Titanic still fascinates. For more math media resources, go to http://www.media4math.com.

2. Why the Titanic Sank
The Titanic was a British ship that set sail on April 10, 1912. It made two
stops before heading toward New York. It never made it there. It sank on
April 15 after hitting an ice berg.

3. What happened to the Titanic?
Click on this video to see the
sequence of events that led to
the sinking of the Titanic.
http://youtu.be/qCv1jKHfFiY

4. Where is the Titanic now?
Click on this video to see footage
of the wreck of the Titanic.
http://youtu.be/6Z7REEnwKOQ

5. Why the Titanic Sank
To get a sense of how massive the Titanic was, this illustration gives an
idea of the scale of the ship.

6. Why the Titanic Sank
The key to sailing a ship of this size is to make sure the density of the ship
is such that it will float on water. Density is defined as the ratio of mass to
volume.

7. Why the Titanic Sank
The density of water is defined as 1. So in order for the Titanic to float, it
needed a density less than 1.

8. Why the Titanic Sank
To simplify the calculation of density, let’s assume that the bulk of the ship
is in the shape of a triangular prism, as shown here.

9. Why the Titanic Sank
The net on the left shows the three dimensions used to calculate the
volume of a triangular prism.

10. Why the Titanic Sank
The length, width, and height measurements are those of the Titanic. The
mass of the ship was 46,000 tons.

11. Why the Titanic Sank
The measurements provided yield a density of 0.41 for the Titanic, well
below the density needed to float. This also means that the Titanic could
still take on water before sinking.

12. Why the Titanic Sank
Once the Titanic started taking on water, its mass would increase while its
volume decreased. This is shown in the expression above. Losing volume
and gaining mass is a deadly combination that will lead to a ship sinking.

13. Why the Titanic Sank
We can graph the function representing the changing density to see where
it intersects the graph y = 1. This is the point where the ship has taken on
too much water, making its density greater than 1.

14. Why the Titanic Sank
Once the ship gained about 40% more mass in water, then the ship had
too much density to float. One of the features that was intended to prevent
too much water was the set of 16 water-tight sections of the ship.

15. Why the Titanic Sank
However, when the Titanic struck the ice berg, five (possibly six)
compartments were damaged. This would have allowed enough water to
sink the Titanic.

16. Or would it?
Click on this video to see what
additional problems emerged
with these water-tight
compartments.
http://youtu.be/xZ8Olj0xs4Q

17. Why the Titanic Sank
Do you think if the 16 compartments had been fully water tight that the
Titanic might have stayed afloat long enough for the passengers to be
rescued?