Around the earth

Geometry Level 2

A 1.4 meter tall man is walking around the earth along the equator. How much farther, in meters, does his head travel than his feet?

Assumptions:

The shape of the Earth is a perfect sphere.
Take $\pi =\dfrac{22}{7}$ .
The man can walk on water and such.

The answer is 8.8.

6 solutions

Dinesh Nath Goswami
Oct 19, 2015

Let r be the radius of the earth and r+1.4 be the radius from the center of earth to the head of the man.

Therefore the required difference in the circumferences is $2\pi(r+1.4)-2\pi r = 2 \pi (1.4)= \boxed{8.8 m}$

Raj Magesh
Oct 18, 2015

$2\pi(r+\Delta r)-2\pi r = 2 \pi \Delta r = \boxed{8.8}$

This is simple and nice

Nehemiah Osei - 5 years, 7 months ago

Jai Jain
Oct 17, 2015

To find the distance travelled extra by this man, you must take the radius of the Earth =6731

Multiply it by 2 to get the diameter =13462

And add the man's height =13462 + 1.4 =13463.4

To get the distance travelled by his head we now use the Pi * Diameter formula to find the circumference or the length of the path of the man's head = Pi * 13463.4 =42296.5

Subtract the distance of the diameter of the Earth * Pi we get 42296.5 - (Pi * (6731 * 2))

=8.79

Moderator note:

It would be better to express Earth's radius by the value of $R$ , instead of taking it as 6731 in your calculations.

How would the answer change if the equator isn't a perfect circle?

You should have included the man's height twice in the diameter. And Pi is given as 22/7, so you should not use 3.1415... The calculation itself is also wrong: 42296.5 - (Pi * (6731 * 2)) = 4.4 and not 8.79

Ronald Overwater - 5 years, 7 months ago

There's no need to add the mans height twice. The diastance traveled by the tip of his head will be (radius of the earth + the mans height )X 2π

Manisha Garg - 5 years, 6 months ago

U cannot say earth's radius to be 6731. U should hv mentioned it in the question itself about the radius.

Yash Chauhan - 5 years, 8 months ago

The answer does not require you to know the earth's radius.

Janardhanan Sivaramakrishnan - 5 years, 7 months ago

So, the answer is the same whether the man walks around the earth or the moon..?

Nigel James - 5 years, 7 months ago

@Nigel James – This question is even better than the problem!!! Let's assume the Earth has a radius of 12 and the moon has a radius of 5. Then:

C_e=2×22/7×12=75.43

C_(e+1.4)=2×22/7×13.4=84.23

84.23-75.43=8.8

C_m=2×22/7×5=31.43

C_(m+1.4)=2×22/7×6.4=40.23

40.23-31.43=8.8

It doesn't matter what circular object you are on. Your head will always move 8.8 units farther than your feet (if you're 1.4 units tall). Now the real good question is why? :)

Mike Gillespie - 5 years, 7 months ago

@Mike Gillespie – Let's suppose we are walking on a line,How much farther, in meters, does his head travel than his feet? 0 meters? If we suposse the lenght of the equator to be x and we extend the equator as a line of lenght x,How much farther, in meters, does his head travel than his feet?...

Guillermo Templado - 5 years, 7 months ago

@Guillermo Templado – As we are not sure how the universe is "flat" or "curved", it is custom to consider a strait line as a line as an arc with a radius = ∞

Achille 'Gilles' - 5 years, 7 months ago

Michael Mele
Dec 31, 2016

His feet travel directly along the equator of diameter D, and his head travels along a concentric circle of diameter D+2*1.4.

(D + 2.8) * π - D * π = 2.8 * 22/7 = 8.8

Manisha Garg
Nov 23, 2015

Let the radius of the earth be = r

Radius from earth to the head of the walking man = r + 1.4

Distance traveled by foot of man = 2πr

Distance traveled by head of man = 2π(1.4+r)

Difference in distance traveled = 2π(1.4+r) -2πr

= $\frac{2X22X1.4}{7}$

= $\boxed{8.8}$

Achille 'Gilles'
Oct 21, 2015

Around the earth

The answer is 8.8.

6 solutions

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