Question

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Dave Kunst is the first person verified to have completely circled the entire earth on foot which is 23,255 km, in 4 years. Let us assume he travelled in a perfect circle around the earth. Now he digs a tunnel through the centre of the earth penetrating it to other side of earth. How much time approximately will it take for him to go to the other side on foot? (Assume he travels at a constant speed)

Answer of this question - 2.55 years.

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Answer 1

Answer:-

Required time is 2.55 years.

Explanation:-

It is given that Dave Kunst circled the entire earth on foot and covered a distance of 23255 km in 4 years.

Thus, we can understand that :-

∴ Circumference of earth = 23255 km

⇒ 2πr = 23255km

⇒ 2 × 22/7 × r = 23255

⇒ r = 23255×7/44

⇒ r = 3700 km

Thus, radius of is 3700km.

Hence,diameter (d) = 2(3700) = 7400 km.

Now, speed of Dave Kunst :-

⇒ v = 2πr/t

⇒ v = 23255/4

⇒ v = 5813.75 km/yr

______________________________

Now in the 2nd case, it is given that he digs a tunnel through the centre of the earth to travel to another side.

So, we can understand that distance travelled in this case [including return journey]

= d + d

= (7400 + 7400)

= 14800 km

Since speed is contant, thus time taken will be :-

⇒Time = Distance/Speed

⇒Time = 14800/5813.75

⇒Time = 2.55 yr

Answer 2

To find:

Time taken to reach the other side of the Earth if he penetrates a tunnel through the centre of the Earth.

Explanation:

It’s given that he traveled the entire Earth in a perfect circle. Therefore, the total distance covered by him is equal to the circumference of a circle.

To find the time taken by him to reach the other side of the Earth through the centre, we first find the distance between the two sides, which is the diameter of the circle assumed.

Circumference = 2πr

23255 = 2πr

23255 = 2 x 22/7 x r

23255 = 44r/7

23255 x 7 = 44r

162785/44 = r

r = 3699.6 cm

Diameter = r x 2

Diameter = 3699.6 x 2

Diameter = 7399.2 cm

_________________________

Now, taking case 1, where he circled the entire Earth:

Time taken = Distance/Speed

Speed = D/T

Speed = 23255/4

Speed = 5813.7 km/yr

For case 2, where he digs a tunnel through the centre of the Earth:

Total distance = 7399.2 + 7399.2

(Assuming he comes back to the original position)

Total distance = 14798.4 km

Time taken = Distance/Speed

(Given: speed is constant)

T = 14798.4/5813.7

T = 2.5 years