Calculate the future and past height of Mount Everest given its current height and growth rate.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the plate movement calculations:

Question 1: Plate movement calculation
Given:
Current height of Mount Everest = 8,849 m
Growth rate = 5 cm per year = 0.05 m per year
Assumption: "Currently" refers to the year 2023 for calculations involving specific years.

a) What will be the height in 2082? (one decimal place)

Calculate the number of years from 2023 to 2082.
$\text{Years} = 2082 - 2023 = 59 \text{ years}$
Calculate the total height increase over these years.
$\text{Height increase} = 59 \text{ years} \times 0.05 \text{ m/year} = 2.95 \text{ m}$
Add the increase to the current height and round to one decimal place.
$\text{Height in 2082} = 8,849 \text{ m} + 2.95 \text{ m} = 8,851.95 \text{ m}$ $\boxed{\text{8,852.0 m}}$
b) What would be the average height of Mount Everest in 1901? (one decimal place)
Calculate the number of years from 1901 to 2023.
$\text{Years ago} = 2023 - 1901 = 122 \text{ years}$
Calculate the total height decrease over these years.
$\text{Height decrease} = 122 \text{ years} \times 0.05 \text{ m/year} = 6.1 \text{ m}$
Subtract the decrease from the current height and round to one decimal place.
$\text{Height in 1901} = 8,849 \text{ m} - 6.1 \text{ m} = 8,842.9 \text{ m}$ $\boxed{\text{8,842.9 m}}$
c) How long will it take Mt Everest to reach 8,851 m?
Calculate the required height increase.
$\text{Required increase} = 8,851 \text{ m} - 8,849 \text{ m} = 2 \text{ m}$
Calculate the time needed to achieve this increase.
$\text{Time} = \frac{2 \text{ m}}{0.05 \text{ m/year}} = 40 \text{ years}$ $\boxed{\text{40 years}}$
d) What is the projected year for the mountain to reach 8,851 m in height?
Use the time calculated in part (c) and the assumed current year (2023).
$\text{Projected year} = 2023 + 40 \text{ years} = 2063$ $\boxed{\text{2063}}$
Question 2: Plate movement
Given:
YT and KB are on opposite sides of a transform boundary.
Each moves at a rate of 1.5 cm per year in opposed directions.
Relative speed = $1.5 \text{ cm/year} + 1.5 \text{ cm/year} = 3 \text{ cm/year} = 0.03 \text{ m/year}$ .
Current distance between them = 25 meters.
Assumption: "Now" refers to the year 2023 for calculations involving specific years.

a) How long will it take for them to be 55 meters apart? (Answers should be in whole numbers)
Calculate the additional distance they need to move apart.
$\text{Additional distance} = 55 \text{ m} - 25 \text{ m} = 30 \text{ m}$
Calculate the time required for this movement.
$\text{Time} = \frac{30 \text{ m}}{0.03 \text{ m/year}} = 1000 \text{ years}$ $\boxed{\text{1000 years}}$
b) What will be the distance between the two neighbours in 2045?
Calculate the number of years from 2023 to 2045.
$\text{Years} = 2045 - 2023 = 22 \text{ years}$
Calculate the distance increased over these years.
$\text{Distance increased} = 22 \text{ years} \times 0.03 \text{ m/year} = 0.66 \text{ m}$
Add the increased distance to the current distance.
$\text{Distance in 2045} = 25 \text{ m} + 0.66 \text{ m} = 25.66 \text{ m}$ $\boxed{\text{25.66 m}}$
c) What will be the projected distance between them in 17-years from now?
Calculate the distance increased over 17 years.
$\text{Distance increased} = 17 \text{ years} \times 0.03 \text{ m/year} = 0.51 \text{ m}$
Add the increased

Calculate the future and past height of Mount Everest given its current height and growth rate.

Step-by-step solution

Calculate the number of years from 2023 to 2082.

Calculate the total height increase over these years.

Add the increase to the current height and round to one decimal place.

Calculate the number of years from 1901 to 2023.

Calculate the total height decrease over these years.

Subtract the decrease from the current height and round to one decimal place.

Calculate the required height increase.

Calculate the time needed to achieve this increase.

Use the time calculated in part (c) and the assumed current year (2023).

Calculate the additional distance they need to move apart.

Calculate the time required for this movement.

Calculate the number of years from 2023 to 2045.

Calculate the distance increased over these years.

Add the increased distance to the current distance.

Calculate the distance increased over 17 years.

Add the increased

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