Discussion
Tsunami is a shallow water gravity wave. A Tsunami has occurred over the ocean at a distance of about 1100 km from the coast. After how much time will it reach the coast ?
Answer: B
The key's answer is 1 hour 30 minutes, taking a typical open-ocean depth of about 4 km.
A tsunami's wavelength is far greater than the ocean depth, so it travels as a shallow-water wave whose speed depends only on depth d:
\[ \begin{aligned} v &= \sqrt{g d} = \sqrt{9.8 \times 4000} \\ &\approx 198\ \mathrm{m/s} \approx 713\ \mathrm{km/h} \\ t &= \frac{1100}{713} \approx 1.5\ \text{h} \end{aligned} \]
The depth is not stated in the question, so the answer depends on assuming this typical depth; it agrees with the usual figure of 700 to 800 km/h for tsunamis in the deep ocean. One hour would need a speed of 1100 km/h (a depth of about 9.5 km), and two hours or more would need depths of about 2.4 km or less.
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