[tex]\Large{\underbrace{\sf{\orange{Question:}}}}[/tex]
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.
▪️Step by step Explanation required!
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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.
▪️Step by step Explanation required!
━━━━━━━━━━━━━━━━━━━
Note : It would be okay if you don't skip any single step! :D
All the best :)
Answers & Comments
Verified answer
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
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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
Verified answer
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