0
How many times in a day do the hour hand and minute hand point in the same direction?
I just did some tallying in my head, with pencil and paper handy. In a 24 hour day, I count 44 times.
AnswerThe continuous movement of the hour hand brings about something analogous to the "sidereal day" problem. Most of the time, there are 2 occurances per hour of 90 degrees between the hands. But after 2 PM, for example, there is an occurance before 2:30, and the next occurance is 3 PM. There is then one occurance after 3 PM, the next one being after 4 PM. The same thing happens again at 8 and 9. So it seems that a total of 44 is probably right. Another way to 'visualize' that 'twice per hour' can't always work is to see that occurances of 90 degrees must be farther apart than 30 minutes, because both hands are advancing, not just the minute hand. For some hours, the first occurance will be late enough in the hour that the next occurance is in the next hour.
---------------------------------------------------------------------------------------
Let me show you a mathematical approach.
Common sense dictates that the minute hand moves at a faster rate of 5.5 degrees a minute (because the hour hand moves 0.5 degrees a min and the minute hand moves 6 degrees a minute).
We start at 12 midnight. The hands are together. For subsequent 90 degree angles to occur, the minute hand must "overtake" the hour hand by
90 degrees, then 270 degrees, then 360 + 90 degrees, then 360 + 270 degrees, then 360 + 360 +90 degrees.. and so on.
This can be re-expressed as: (1)90, 3(90), 5(90), 7(90), 9(90), 11(90)... n(90).
The number of minutes this takes to happen can be expressed as (1)90/5.5, 3(90)/5.5, 5(90)/5.5, 7(90)/5.5, 9(90)/5.5, 11(90)/5.5... n(90)/5.5.
In one day, there are 24 hr * 60 mins = 1440mins
To find the maximum value of n,
n(90)/5.5 = 1440
n = 88
but as seen from above, n must be an odd number (by pattern recognition and logic)
hence n must be the next smallest odd number (87)
counting 1,3,5,7,9,11......87, we see that the number of terms = (87-1)/2 +1 = 44.
In other words, the minute hand "overtakes" the hour hand on 44 occasions in 24 hours in order to give a 90 degree angle.
Therefore the answer to your question is 44.
What else can I help you with?
How many times during a 12 hour period from noon to 1159 does the minute hand point exactly the same direction as the hour hand?
Eleven (11) times, counting the one at Noon.
How many inches does it takes a minute hand to travel in one hour?
The distance depends on how far the relevant point on the minute hand is from its point of rotation. This is because the motion of the minute hand is angular, not linear.
How many times minute hand rotate in 24 hours?
Minute hand will rotate 1440 times in 24 hours.
Where does the minute hand point at 815?
At the 3.
How many times are the second minute and hour hand in the exact same place?
Disregarding the second hand (for a few seconds), the hour and minute hands overlap (point in the same direction) 22 times in a 24 hour period. It happens once after every hour except the 12 o'clock hour. After 12 o'clock, the next occurance is after 1 o'clock. The fractions of a minute required for these overlaps do not always coincide with the number of seconds that the second hand would have to register in order for the second hand to 'join' the hour and minute hands. The only times that all three hands are perfectly overlapping (pointing in the same direction) is at 12 midnight and 12 noon. So the second minute and hour hands are in the exact same place only twice during every 24 hour period. The hour and minute hands join each other every 65.454545 minutes, or 32.727272 degrees. The minute hand advances 163.636363 degrees each time the hour and minute hands overlap.
Where does the minute hand point at 4.45?
It points at the 9.
What are the times of the day when the hour hand is perpendiccular to the minute hand and the minute hand points to the 12?
3:00 or 9:00
At what times does the minute hand pass the hour hand?
youre mom
Where does the minute hand point on ten past 8?
twelvtey
Where does the minute hand point at 10 to 6?
10 (coincidence)
If the minute hand is pointing to the twelve and the hour hand is perpendicular to the minute hand what two times could it be?
It could be four times per day: 9 AM, 9 PM, 3 AM, and 3 PM. Note: The question as stated is false and would likely cause controversy if it was on an important exam. The question should be "If the minute hand is pointing to the twelve and the hour hand is perpendicular to the minute hand, what times could it be?"
How many times does the hour hand and minute hand cross in 12 hour period of time?
The minute hand will cross over the hour hand once every hour. So in 12 hours, the answer is 12 times.
