Question

Here is a less obvious example of a linear function. Imagine putting a rope around the Earth. Make it nice and snug. Now add 33 m to the length of the rope and arrange it concentrically around the Earth. Could you walk under it without hitting your head? Justify your answer.

Answer 1

A person who has height less than 5.2521 m can walk under the rope without hitting his/her head.

Explanation:

Radius of earth = R

Length of rope around Earth = Circumference of Earth = 2πR

Now add 33 m to the length of the rope that means to increase the circumference

C = 2πR+33

Now,

C = 2πR'

⇒2πR' = 2πR+33

In order to find the height we need to find difference of the radii

⇒2πR'-2πR = 33

`\\\Rightarrow R'-R=(33)/(2\pi)\\\Rightarrow R'-R=5.2521\ m`

So, a person who has height less than 5.2521 m can walk under the rope without hitting his/her head.