Question

1. we measure time based on the rotation of the earth → one rotation of the earth is equal to one day. the spin of the earth is slowing down, so the length of our day is gradually getting longer. each century, the length of the day increases by .0015 of a second. if the length of a day in 1998 is equal to 23 hours and 56 minutes, how long will a day be in the year 16,001,998?

Explanation:

Step1: Calculate number of centuries

Find the number of centuries between 1998 and 16001998.
$n=\frac{16001998 - 1998}{100}=160000$

Step2: Calculate total increase in seconds

Multiply number of centuries by increase per century.
$\text{Increase}=n\times0.0015 = 160000\times0.0015=240$ seconds

Step3: Convert initial time to seconds

$23$ hours and $56$ minutes is $23\times3600+56\times60 = 82800 + 3360=86160$ seconds

Step4: Calculate new time in seconds

Add the increase to the initial time in seconds.
$\text{New time}=86160 + 240=86400$ seconds

Step5: Convert new time back to hours and minutes

$86400\div3600 = 24$ hours

Answer:

24 hours