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can you y'all please answer this question Example 16.3 Tsunami! A tsunami (sometimes mistakenly called a tidal wave) is an ocean wave, but it differs
can you y'all please answer this question
Example 16.3 Tsunami! A tsunami (sometimes mistakenly called a tidal wave) is an ocean wave, but it differs in many respects from normal ocean waves lapping at the shore. A tsunami is created by an underwater earthquake or landslide, and it can be modeled, as shown in Figure 16.99, as a single wave pulse traveling outward from the source at speed 71. A tsunami traveling across the open ocean is very wide (w a: 200 km z 120 mi) and not at all tall (h z 1 m). A tsunami passes beneath ships at sea as a minor swell that is not even noticed. Because the ocean depth d is much smaller than the width of the tsunami pulse, a tsunami is classied as a shallow-water wave. It can be shown that the speed of a shallow-water wave is v = \\/gd. A tsunami slows as it approaches land because the ocean depth decreases. Cars on a highway get more bunched together when they encounter an obstacle that forces them to slow down. Similarly, the width of the tsunami pulse gets smaller as it slows; it can be shown that the width is directly proportional to the speed: w cc v. Figure 16.9 A tsunami can be modeled as a wave pulse. D is a. The average depth of the open ocean is 4000 m. What is the average speed of a tsunami in the open ocean? How long does it take a ZOO-kmwide tsunami to pass beneath a ship? b. What are the speed and width of this tsunami as it enters a harbor with a depth of 10 m? c. What is the height of the tsunami in the harbor? How long does it take to move onshore? SOLVE a. The tsunami's speed as it travels through the 4000-mdeep ocean is V (9.8 mlsz)(4000 m) 200 m/s w 450 mph Vocean = \\/g_d This is nearly the speed of a jet ying over the ocean! At this speed, a ZOO-kmwide pulse passes beneath a ship in a time of Wocean 200,000 In . A = = = 1000 m 16 ' vocean 200 m/s 3 mm A 1-mhigh swell that takes 8 min to rise and another 8 min to fall will certainly not be noticed. b. As the ocean depth decreases to 10 In, the tsunami slows to a speed of vharbo, = (9.8 m/sz)(10 m) = 10 m/s w 20 mph This is more typical of the speed of ordinary ocean waves approaching the shore. The pulse width is proportional to the speed, so we can use ratios to write Wharbor wocean Vharbor Vocean Thus the width of the tsunami in the harbor, as it reaches the shore, is Vharbor 10 ms = X = X 200 km = 10 km Wharbor Wocean 200 III/S Vocean This is still a very wide pulse of water, although much smaller than the 200 km width in the open ocean. . Water is nearly incompressible. As the width of the pulse narrows, the pulse has to get taller to account for the volume of water in the pulse. In our one-dimensional model, the area of the pulse, which is proportional to width X height, must remain constant. Thus wharbor X hharbor = Wocean X hocean We can calculate that the height of the tsunami in the harbor is ocean 2001011 wharbor The time it takes this pulse of water to come ashore is _ Wharbor 10,000 m =1000$ m 16min vharbor 10 III/S AtStep by Step Solution
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