Answer :
The Big Island of Hawaii will take approximately 0.243 years or 2.92 months to reach the subduction zone off Japan if the "Pacific Plate Express" operates without change.
Given, the following table of the islands: Name of Island Kure Midway Necker Kauai Distance from Kilauea (km) 2600 2550 1000 600 Age 31 25 12 5 3To calculate:
(A) The average rate of plate motion since Kure Island formed in cm/yr. The distance between Kure Island and Kilauea = 2600 km The age of Kure Island = 31 myr=31×106 yearsDistance = Speed × Time Thus, the average rate of plate motion since Kure Island formed = Distance / Time= 2600000000 cm / (31×106 years)= 84.516 cm/yr Thus, the average rate of plate motion since Kure Island formed in cm/yr is 84.516 cm/yr.
(B) The average rate of plate motion since Kauai formed in cm/yr. The distance between Kauai and Kilauea = 600 km The age of Kauai = 5 m yr=5×106 years Distance = Speed × Time Thus, the average rate of plate motion since Kauai formed = Distance / Time= 60000000 cm / (5×106 years)= 12 cm/yr Thus, the average rate of plate motion since Kauai formed in cm/yr is 12 cm/yr.
(C) The Pacific plate was moving at an average rate of 84.516 cm/yr since Kure Island formed and at an average rate of 12 cm/yr since Kauai formed. The Pacific plate has been moving slower during the last 5 my as compared to the last 26 my since it was moving at an average rate of 84.516 cm/yr over the last 26 m.y. and at an average rate of 12 cm/yr over the last 5 my.
(D) The total average rate since Kure Island formed = 84.516 cm/yrIn 1 year, the plate moves a distance of 84.516 cm In 50 years, the plate moves a distance of 84.516 × 50= 4225.8 cm or 42.258 m Thus, the Pacific Plate will move 42.258 m in 50 years using the total average rate since Kure Island formed.
(E) The trajectory of the Pacific Plate currently points towards Japan, approx. 6500 km away. Distance between Japan and Hawaii = 6500 km Distance traveled in 1 year at an average rate of 84.516 cm/yr = 84.516 × 365×24×60×60 cm= 2.67 × 1012 cm= 26700000 m Thus, the time taken to travel a distance of 6500 km= 6500000 m / 26700000 m/yr= 0.243 years
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