Beastmode Question

You see me twice a minute, thrice an hour and geometrically equal to the time elapsed. If the sun rise at x m/sec and the cloud run through the sky at y m/sec, find the maximum RADIUS OF THE EARTH.

To find the maximum radius of the Earth, we need to solve for the variables in the given information. Let's break down the question step by step:

1. "You see me twice a minute, thrice an hour": This means that whatever is being referred to, you see it twice in a minute and three times in an hour. From this, we can infer that it is a periodic occurrence that repeats every hour. Let's call the time period T.

2. "Geometrically equal to the time elapsed": This implies that the time it takes for the occurrence to repeat is equal to the time that has passed since it started. In other words, T is equal to the time elapsed.

3. "If the sun rises at x m/sec and the cloud runs through the sky at y m/sec": This information about the sun and cloud is unrelated to the question and can be disregarded for now.

Let's focus on the key phrase, "You see me twice a minute, thrice an hour, and geometrically equal to the time elapsed." This provides insight into the periodic occurrence we are trying to determine.

If the time period T is equal to the time elapsed, and we see this occurrence twice every minute, then T must be a multiple of one minute (60 seconds). Since it also occurs thrice in an hour, T must be a multiple of one hour (3600 seconds).

To find the maximum radius of the Earth, we need to determine the value of T that satisfies both conditions:

T = multiple of 60 seconds
T = multiple of 3600 seconds

The least common multiple (LCM) of 60 and 3600 will give us the value of T. Let's calculate it:

LCM(60, 3600) = 3600 seconds

Therefore, T = 3600 seconds.

Finally, we can use the formula for the circumference of a circle to find the maximum radius of the Earth. The circumference of a circle is given by C = 2πr, where r is the radius.

C = 2πr
3600 = 2πr

To solve for r, divide both sides of the equation by 2π:
r = 3600 / 2π

Calculating this in decimal:

r ≈ 572.958 m

Therefore, the maximum radius of the Earth is approximately 572.958 meters.