Show that the minute hand of awatch gains 5°30' on the hour hand in a minute
done by Steve 5 years ago
http://www.jiskha.com/display.cgi?id=1341112400
You are mad
To show that the minute hand of a watch gains 5°30' on the hour hand in a minute, we need to calculate the angular displacement of each hand during that time.
First, let's calculate the angular displacement of the minute hand. In one minute, the minute hand moves 360° around the dial (since there are 60 minutes in an hour, and the watch dial represents a full circle of 360°). Therefore, the minute hand moves 360°/60 = 6° per minute.
Next, let's calculate the angular displacement of the hour hand in one minute. There are 60 minutes in an hour, and since the hour hand takes 12 hours to complete a full rotation, it moves 360°/720 = 0.5° per minute.
Now, let's see how much the minute hand gains on the hour hand. The difference in angular displacement between the two hands is 6° - 0.5° = 5.5° per minute.
Since there are 60 minutes in an hour, the minute hand gains 5.5°/min * 60 min = 330° in an hour.
To express this angular gain in degrees and minutes, we know that there are 60 minutes in a degree. So, the minute hand gains 330° * 60 min/degree = 19800 minutes in an hour.
We can convert this to degrees and minutes by dividing by 60. 19800 min / 60 = 330 degrees.
Therefore, the minute hand gains 330° on the hour hand in an hour. This is equivalent to 5°30' (since there are 60 minutes in a degree and 60 seconds in a minute).
Hence, we have shown that the minute hand of a watch gains 5°30' on the hour hand in a minute.