in a clock how many times 90 degree are made between minute and hour hand.?

Question

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Answer 1

If you have a true analog clock with smooth movement of the hour and minute hands, the math is as follows:

Each hour, the hour hand moves 1/12 of a circle (360 degrees), or 30 degrees.

Each hour, the minute hand moves a full circle (360 degrees).

Each minute, the hour hand moves 1/60 of 30 degrees (the movement of the hour hand in an hour), or 0.5 degrees.

Each minute, the minute hand moves 1/60 of 360 degrees (the movement of the minute hand in an hour), or 6 degrees.

12:00: hour = 0.0 degrees, minute = 0 degrees, difference = 0.0 degrees
12:01: hour = 0.5 degrees, minute = 6 degrees, difference = 5.5 degrees
12:02: hour = 1.0 degrees, minute = 12 degrees, difference = 11.0 degrees
12:03: hour = 1.5 degrees, minute = 18 degrees, difference = 16.5 degrees
12:04: hour = 2.0 degrees, minute = 24 degrees, difference = 22.0 degrees
12:05: hour = 2.5 degrees, minute = 30 degrees, difference = 27.5 degrees
12:06: hour = 3.0 degrees, minute = 36 degrees, difference = 33.0 degrees
12:07: hour = 3.5 degrees, minute = 42 degrees, difference = 38.5 degrees
12:08: hour = 4.0 degrees, minute = 48 degrees, difference = 44.0 degrees
12:09: hour = 4.5 degrees, minute = 54 degrees, difference = 49.5 degrees
12:10: hour = 5.0 degrees, minute = 60 degrees, difference = 55.0 degrees
12:11: hour = 5.5 degrees, minute = 66 degrees, difference = 60.5 degrees
12:12: hour = 6.0 degrees, minute = 72 degrees, difference = 66.0 degrees
12:13: hour = 6.5 degrees, minute = 78 degrees, difference = 71.5 degrees
12:14: hour = 7.0 degrees, minute = 84 degrees, difference = 77.0 degrees
12:15: hour = 7.5 degrees, minute = 90 degrees, difference = 82.5 degrees
12:16: hour = 8.0 degrees, minute = 96 degrees, difference = 88.0 degrees
12:17: hour = 8.5 degrees, minute = 102 degrees, difference = 93.5 degrees

Therefore, between 12:16 and 12:17, the hour hand and minute hand were 90 degrees apart.

If you notice the gain that the minute hand makes on the hour hand, you will see it is 5.5 degrees per minute.

Take 90 degrees and divide by 5.5 degrees per minute and you get 16.3636 minutes which is the rate at which the minute hand advances 90 degrees from the hour hand.

The first occurance is 12:16.36.
The second occurance is 12:49.06 and every 32.72 minutes from there on until you reach 12 again.

There are 720 minutes in 12 hours, so 720 minutes / 16.3636 minutes per 90 degree increments is 44.

Divide by 2 to get rid of the occurrences of the 0 and 180 degree angles and the answer is 22 in 12 hours.

Answer 2

When the clock is showing 6:15, the hour hand is not directly over the 6 mark on the clock. The hour hand moves at a rate of 30 degrees per hour (due to the fact that there are 12 markings at at total of 360 degrees [360/12]). Then you find how much it moves per minute so 30 / 60 which means 1/2 a degree per minute. If the hour hand were not to move when the minute hand reached at 15 minutes, the degree would be exactly 90. Now add how many degrees the hour hand moves in 15 minutes. This would be 15 times 1/2 or 7 degrees 30' (30' = 30 minutes [a sophisticated way of saying half a degree]) So now you can say that the angle between them is 90 degrees + 7 degrees and 30 minutes which equals 97 degrees and 30 minutes.

Answer 3

Edit: tlbs101 has the right answer. It *should* happen twice an hour but 3:00 and 9:00 screw it up, because that means that the hour before it only has 1. So he's right, 22 per 12 hours, or 44 in a day.

Wrong:
It happens twice every hour, so 48 in a day. Think about it, start at noon. Around 12:15/16 there's a right angle, and then again around 12:45-50. This happens for every hour.

Answer 4

Within a 12-hour period, 22 times:

12:16:25
12:49:05
1:21:50
1:54:35
2:27:15
3:00:00
3:32:45
4:05:25
4:38:10
5:10:55
5:43:40
6:16:20
6:49:05
7:21:50
7:54:35
8:27:05
9:00:00
9:32:45
10:05:25
10:38:10
11:10:55
11:43:35

(all times within 5 seconds of the actual 90 degree point)

.

Answer 5

24 x 2 = 48

cuz if at one position it make a 90 degree, few time later, after the rotation of minute hand of about 180 + some more degerees, they would again right handed within same houd.

so
2 times right angled each hour.
total


24 x 2 = 48

Answer 6

Think about it.

The hands move continuously between each tick-mark (minute marks). SO for every position on the clock so marked as one hand lines up with each mark, the other can, at some point, move smoothly thru the marks as well and align to make a 90 degree angle. So the answer is 60, but if you think about it, the hands would align fore more than that since you could conceivably make finer marks between each minute mark.

But on a standard analog clock......60.

Answer 7

Infinte amount. As time keeps going, more 90 degree angles are created. It doesn't end until time ends.

Answer 8

Twice per hour.

Answer 9

60, I believe.