Problem 10 Phase velocity and group velocity for atsunami ESG 281 11/17/2022 For water waves of long wavelength on deep water, the 03 vs. k relation is: (1) (o = (gk)y2 for 9 2 17 mm (these are called 'gravity waves') g = 9.8 m/s2 (for shorter wavelengths, surface tension is important and the relation is different) a) For (1) Calculate \"(aphase (k) and 'Ugroup (k) b) For (1), evaluate uphase and vgroup for 7 = 200m (which could be produced in a wind-driven storm at sea) and 7 = 200km (a typical wavelength for a tsunami). Give the answers in m/s and miles/hour. c) How long would a pulsed tsunami wave with a main wavelength 7L = 200 km take to reach California from Japan (say, approximately 8500km)