Question

Tsunamis: Wavelengths for Tsunamis can extend for 100's of kilometers and their wave periods from tens of minutes to hours. Because the wavelengths far exceed ocean depth, we use the Shallow-Water Wave formula, where velocity (v) is derived by taking the square root of the product of the acceleration of gravity (8 = 9.8 meters/second) and water depth (d) in meters: v in m/s = g. Or, because g is constant, we can modify the formula using the square root of g: v = 3.13a 8. A large earthquake occurs off the coast of Chile, South America, along the Peru-Chile Subduction Zone. The earth movement causes a Tsunami that propagates in all directions. Calculate the velocity of the Tsunami using the formula above. For depth (d), use the mean depth of the Pacific Ocean: 4000 meters. For units: note the units used for gabove. (Show your work) 9. The Pacific Ocean Basin has a Tsunami Warning System that alerts countries to the danger of the powerful wave. Now that we have the wave velocity, we can estimate time of travel to locations in the wave's path to allow them to take the necessary precautions. (Hint: review worksheet 4, question #10, for how to calculate time when velocity and distance are known) Note: Time calculations are in hours, so you will need to convert from seconds. There is more than one way to do it! Estimate the time it will take (in hours) for the Tsunami to reach the following three locations (show your work):

a. Lima, Peru: 2,435km distance from Tsunami origin
b. Cabo San Lucas, Mexico: 7,300km distance from Tsunami origin
c. Hilo, Hawaii: 10,480km distance from Tsunami origin

Answer 1

The velocity of a tsunami with a depth of 4000 meters is calculated as 198 m/s using the shallow-water wave formula. The estimated travel times to Lima, Peru, Cabo San Lucas, Mexico, and Hilo, Hawaii are approximately 3403.52 hours, 10241.30 hours, and 14702.58 hours, respectively, when the velocity is divided by each location's distance from the origin.

Step-by-step explanation:

To calculate the velocity of a tsunami using the shallow-water wave formula, we use the square root of the product of the acceleration of gravity (g = 9.8 m/s2) and the water depth (d).

Velocity (v) is given by the equation v = √(g × d). Using the mean depth of the Pacific Ocean (4000 meters), the velocity can be calculated as follows.

v = √(9.8 m/s2 × 4000 m) = √(39200 m2/s2) = 198 m/s

For the time of travel, time (t) is equal to distance (s) divided by velocity (v).

• To Lima, Peru: t = 2435 km / 198 m/s = 12272727.27 s = 3403.52 hours
• To Cabo San Lucas, Mexico: t = 7300 km / 198 m/s = 36868686.87 s = 10241.30 hours
• To Hilo, Hawaii: t = 10480 km / 198 m/s = 52929292.93 s = 14702.58 hours

Note that the wave time must be converted from seconds to hours by dividing the result by 3600 (the number of seconds in an hour).