At what time after 10:30 will the hands of a clock first be perpendicular?

Answer 1

At 10:30, the hour hand is at a 45 degree angle to the horizontal, halfway between the 9 and the 12. Sometime between 10:37 and 10:40, the minute hand will swing through the zone where it would be perpendicular to the hour hand, between a 45 and 50 degree angle to the vertical.

The hour hand moves 1/12 of a circle each hour, which is 30 degrees every 60 minutes. Therefore, for every minute after 10:30, the hour hand will move 0.5 degrees, so the angle to the horizontal will be 45+(0.5)t, where t=the number of minutes past 10:30.

However, the minute hand moves 6 degrees per minute (60 minutes = 360 degrees) after 10:30, so the angle from the vertical will be 6t.

The hands are perpendicular when the hour hand's angle from the horizontal is the same as the minute hand's angle from the vertical.

45+(0.5)t = 6t
45 = 5.5t
t = 45/(5.5) = 8.18181818...

... which is 8 minutes, 10.909090909 seconds.

Therefore, the hands will be perpendicular just after 10:38 (about 11 seconds afterwards).

Answer 2

It will be at 10:38 and 2/11 minutes.

The hour hand travels m/2 degrees every m minutes. The minute hand travels 6m degrees every m minutes.

The angle between 9:00 and the desired number of minutes after 10:00 for the hour hand will be 30 + m/2.

The angle the minute hand traveled between 9:00 and the desired number of minutes after 9:00 will be 270 - 6m

So (30 + m/2) + (270 - 6m) = 90

Answer 3

The position, in degrees, of the hour hand is x/12*360 and the position of the minute hand is (x-10)*360. The two will be perpendicular when (x-10)*360=x/12*360-90
or: x-10=x/12-.25
11x/12=9.75
x=12*9.75/11
x=10.636
or at 10:38.16

Answer 4

If 0 degree is on 12 hours and we measure clock wise, we have, at 10:30, minute hands at 180 degree and hour hand at 315 degree. So difference is 135 degree. We want the difference to be 90, so we need do decrease by 135-90 = 45.
In one minute the minute hand makes 360/60 = 6 degree
In one minute the hour hand makes 360/12/60 = 0.5 degree (this is why at 10:30 hour hand is at 315).
So, in one minute, the difference decreases by 5.5 degree.
So we need 45/5.5 minutes to have 90 degree difference.
45/5.5 = 8 min and 10.9 sec.
So answer is 10:38:10.9

Answer 5

3:00, 9:00, in basic terms 4. and that's actual. am and pm. perpendicular skill intersecting at a ideal perspective. it won't be in a position to be six o'clock in view that could form a a hundred and eighty diploma perspective. that may no longer a ideal perspective. have faith me, this one is sweet. whilst a clock is at 6:15, the hour hand strikes off the six via slightly, making it decrease than ninety levels.

Answer 6

10:45 (or just a little after to compensate for the fact that the hour hand will be slightly past the 30.)

Answer 7

12:15

Answer 8

10:35

Answer 9

10:33

Answer 10

10 35

the clocks have distances of 30 degrees between two consecutive numbers