Answer :
Final answer:
The average rate of motion of the Pacific Plate in cm per year, calculated by dividing the distance of Kauai from the hotspot (converted to centimeters) by Kauai's age (in years), is approximately 9.27 cm/year.
Explanation:
To calculate the average rate of motion of the Pacific Plate in cm per year concerning Kauai and the current hotspot, we use the given parameters: Kauai is approximately 473 km from the hotspot and is 5.1 million years old. To find the rate of motion, we first convert the distance from kilometers to centimeters (473 km * 100,000 cm/km = 47,300,000 cm). Then, we divide by the age of Kauai in years (5.1 million years * 1,000,000 years/million years = 5,100,000 years). The formula for the average rate of motion is:
Rate of motion (cm/year) = Distance (cm) / Time (years)
Plugging in the values gives us:
Rate of motion (cm/year) = 47,300,000 cm / 5,100,000 years
Finally, we compute the rate:
Rate of motion (cm/year) = 9.27 cm/year (rounded to two decimal places).
This represents the average speed at which the Pacific Plate has moved away from the hotspot, carrying Kauai with it, over the past 5.1 million years.
Answer:
9.274 cm per year.
Explanation:
Given:
Island of Kauai used to sit on the hot spot; it is approximately 5.1 million years old.
And 473 km away from the hot spot.
Question asked:
Given these parameters, what is the average rate of motion of the Pacific Plate in cm per year?
Solution:
First of all we will change the distance 473 Km into cm,
As we know that, 1 km = 100000 cm
473 km = [tex]473\times100000=47300000= 473\times10^{5}[/tex]
Here time span is also given, 5.1 million years old, we can write this as,
[tex]5.1\times10^{6}\ years[/tex]
Now, average rate of motion of the Pacific Plate can be determined by dividing the distance traveled by plates from its time span.
Average rate of motion of the Pacific Plate = [tex]\frac{473\times10^{5} }{5.1\times10^{6} } \\[/tex]
= [tex]\frac{473\times10^{5} }{5.1\times10\times10^{5} } \\[/tex]
=[tex]\frac{473}{51} =9.274\ cm\ per \ year[/tex]
Therefore, he average rate of motion of the Pacific Plate is 9.274 cm per year.
