Question

Dave Kunst is the first person verified to have completely circled the entire earth on foot in 4 years. Let us assume he traveled in a perfect circle around the earth and the center of his circle is same as the center of the earth. If he traveled through a tunnel through the center of the earth penetrating to other side of earth at the same average speed, how much time would he have taken?

Solution

Let 'D' be the diameter of the Earth.

Then, distance covered will be the perimeter of the circle,

d=πD

Time taken, t=4 years

From defintion of speed,

v=dt

v=πDt......(i)

If he travelled across the tunnel, he would cover a distance equal to the diameter of the earth. So, new distance is:

d′=D

Let new time taken be t′.

It is given that the speed of the man in both the cases is same. Hence, again using defintion of speed,

v=d′t′

v=Dt′......(ii)

Equating (i) and (ii), we get:

πDt=Dt′

t′=tπ

t′=4π

t′=1.27 years

Then, distance covered will be the perimeter of the circle,

d=πD

Time taken, t=4 years

From defintion of speed,

v=dt

v=πDt......(i)

If he travelled across the tunnel, he would cover a distance equal to the diameter of the earth. So, new distance is:

d′=D

Let new time taken be t′.

It is given that the speed of the man in both the cases is same. Hence, again using defintion of speed,

v=d′t′

v=Dt′......(ii)

Equating (i) and (ii), we get:

πDt=Dt′

t′=tπ

t′=4π

t′=1.27 years

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