For the Algebra Teacher: Six Algebra Problems Based on World War II Naval and Military Applications

Designing and presenting interesting math problems can be very challenging for the Algebra teacher. One complaint I would often hear from my Algebra students was the age-old whine "When am I ever going to use this?!" I wish I had known back then about the book I have in my hand right now: "Spherical Trigonometry with Naval and Military Applications" published in 1942. Within the first chapter I found a wealth of real life math problems based on naval and military situations. Explaining to your math class that these problems were actually used to train officers in the US Army and Navy during World War II can help make learning math (particularly Algebra) relevant and interesting for your class.

Naval and Military Application Algebra Problem #1: Calculate Air Pressure
If the air pressure on the ground is 14.7 lb/sq. in. the pressure P at height h ft. is given approximately by:

P = 14.7e^-0.0000377h

Find the air pressure at the height of (a) 10,000 ft., and (b) 15,000 ft.

Naval and Military Application Algebra Problem #2: Calculate Force Exerted on a Parachuting Man
If the force F exerted by a parachute on a man of weight W lb. falling v ft/sec is given by:

F = (W*v)/15

find the forced exerted on a 160-lb. man by a parachute just as it opens if he is then falling at 98 ft/sec.

Naval and Military Application Algebra Problem #3: Calculate Vertical and Horizontal Distance for Dropping a Bomb
A plane descending with a speed of 120 mph at an angle of 20 degrees with the horizontal drops a bomb when 700 ft high. The vertical distance y and the horizontal distance x of the bomb from the point of release are given by the equations:

y = 60.2*t + 16.1*t²
x = 165.4*t

(a) Find the distance the bomb moves horizontally if it strikes the warship in 4.98 seconds.
(b) Find the vertical distance the bomb falls during the first 2.5 seconds.

Naval and Military Application Algebra Problem #4: Calculate a Torpedo's Total Time
1 nautical mile is 2027 yards. A "knot" is a measure of speed equal to "nautical miles per hour." Assuming the speed of the torpedo is constant, find the total time required for a 23.8 knot torpedo to make its maximum run of 12,640 yards.

Naval and Military Application Algebra Problem #5: Calculate Time for a Warship to Close With an Enemy Scout
The captain of a warship wanted to come as close to an enemy scout as possible. The time in hours required to attain this position is given by the formula:

Time = (b*c)/(a*(a²-b²)^(1/2))

where a = speed in knots of the scout, b = speed in knots of the warship, and c = initial distance of the scout from the warship. Find the time required if a = 32.7 knots, b = 28.4 knots, and c = 20.9 nautical miles.

Naval and Military Application Algebra Problem #6: Calculate the Height of a Projectile
If the height y in feet of a projectile above a horizontal plane at time t seconds is given by the equation:

y = -16*t² + 600*t

(a) Find the height of the projectile at 18.75 seconds.
(b) Find the height of the projectile at 25 seconds.

Concluding Notes
When I was checking the answers in the back of the book for these problems I found a basic math error. For this reason I decided not to include the book answers for these problems. I would expect the math teacher to double and triple check his or her answers, anyway, before presenting these problems to the class.

These particular math problems were taken from Chapter I: Logarithms. During the time this book was written the math student would not have had access to personal calculators and therefore would have been expected to look up and calculate logarithms by hand, using extensive logarithmic tables. If one of your teaching goals is to teach about math history, consider trying to track down one or more of these books of logarithm tables and demonstrate how a naval navigator or bomber pilot would have been taught to compute a logarithm during World War II.

Blessings!

Source
Lyman M. Kells, Willis F. Kern and James R. Bland. Spherical Trigonometry with Naval and Military Applications