The Second Time the Clock Hands Are Perpendicular: An SEO-Optimized Guide for Google SEO Experts

chuyên gia SEO t? Google, h?y cùng tìm hi?u v? cách troochn ch? ra th?i ?i?m th? hai mà tay can và tay phút c?a ??ng h? song song nhau qua bài vi?t này. Giáo trình này kh?ng ch? giúp b?n hi?u r? h?p d?n cho ng??i ??c, mà còn giúp t?i ?u hóa n?i dung nh?m c?i thi?n th? h?ng trên Google.

Understanding the Positions of the Clock Hands

In SEO content creation, it's essential to explain concepts in a clear and understandable manner. The minute hand moves at a rate of 6 degrees per minute, while the hour hand moves at a rate of 0.5 degrees per minute. These rates are crucial for solving the problem of when the clock hands will be perpendicular for the second time.

Initial Positions at 5:00

The initial positions of the clock hands are as follows:

The minute hand is at 0 degrees. The hour hand is at 150 degrees, which is 5 times 30 degrees (since each hour represents 30 degrees).

How to Find Perpendicular Angles

The hands of the clock are perpendicular when they are 90 degrees apart. This can happen in two scenarios:

The minute hand is 90 degrees ahead of the hour hand. The hour hand is 90 degrees ahead of the minute hand.

Setting Up the Equations

Let's denote m as the number of minutes after 5:00. The positions of the hands can be expressed as follows:

The position of the minute hand at m minutes is 6m degrees. The position of the hour hand is 150 0.5m degrees.

To find the first case where the minute hand is 90 degrees ahead of the hour hand:

6m - (150 0.5m) 90

Solving for m gives:

5.5m 240

m 240 / 5.5 ≈ 43.64 minutes, which is approximately 5:44.

To find the second case where the hour hand is 90 degrees ahead of the minute hand:

150 0.5m - 6m 90

Solving for m gives:

150 - 5.5m 90

5.5m 60

m 60 / 5.5 ≈ 10.91 minutes, which is approximately 5:11.

Conclusion

The hands of the clock are perpendicular for the second time approximately 43.64 minutes after 5 o'clock, making it around 5:44.