Investigation: Modeling tsunami movement

Objectives

• To work with a radical function.
• To practice simplifying radicals.

Materials

• Paper
• Pen
• Internet
• Calculator

Procedure

Tsunamis are series of large ocean waves that can be caused by an underwater volcanic eruption, earthquake or landslide. Tsunamis are dangerous because they can reach up to 500 miles per hour. Due to the enormous threat a tsunami poses, it is important for scientists to track any possible tsunamis that may be occurring. Several tsunami research facilities exist that constantly monitor the movement of the waves in the oceans to ensure that they can give warning to the areas that are in danger. There are two equations that are important for monitoring tsunamis:

1. s=\sqrt{ g \times d} where s=speed in meters per second, g=acceleration due to gravity (9.8 meters per second^2 ) and d= depth of the ocean in meters
2. t=\frac{d}{s}  where t= the tsunami’s travel time to shore in seconds, d= the distance to shore in meters, and s=the speed at which the tsunami is traveling in meters per second

In this investigation we will be investigating how fast tsunamis move and how long it takes them to reach varying locations using these equations.

Questions

1. What would be the speed of a tsunami that was located in a part of the ocean that is 1200 meters deep?
   • First give your answer in exact (radical) form. If possible, simplify your answer.
   • Then give your answer in decimal form.
   • Is the speed a rational or irrational number?
2. What would be the speed of a tsunami that was located in a part of the ocean that is 2400 meters deep?
   • First give your answer in exact (radical) form. If possible, simplify your answer.
   • Then give your answer in decimal form.
   • Is the speed a rational or irrational number?
3. Is the speed of the tsunami at a depth of 2400 meters double the speed of the tsunami located at a depth of 1200 meters? Why or why not?
4. Work with a friend to answer the last questions:  
5. Suppose that an earthquake hits at the coordinates 40N, 140W . Assume that the depth of the water at the epicenter of the tsunami is 4500 meters. How long will it take for the tsunami to reach Santa Barbara, California? How long will it take to reach San Francisco, California?

1. Helpful Hint!

   To find the distance from the epicenter to the city you can look up the latitude and longitude of the city and then create a right triangle using the difference in latitudes as one leg and difference in longitudes as the other leg. Then solve for the hypotenuse and use the map scale to turn this into kilometers. Or, you can use a map application online to measure the distance.

2. Would the tsunami take longer to reach Santa Barbara or San Francisco?
3. Why is it important to be able to determine the amount of time it will take a tsunami to reach different locations?