clock problem?

Question

7:00 & at what time will small and big hand of the clock will meet.? when it will become a right angle? &when it will form a 180 degrees.

Answer 1

If you need the time between 7:00 & 8:00 for the hands to form a particular angle.

We need to convert angle to minutes(time)
0° ≡ 0 minutes(time) ,... 90° ≡ 15 minutes(time),
180° ≡ 30 minutes(time)

Consider the time 7:x , where x is the minutes past 7.

If the minute hand has traveled x minutes, the hour hand has traveled only x/12 minutes. The hour hand is 1/12 of the speed of the minute hand.

If the hour hand is in 7, that means 35 minutes.
The location of the minute hand is in x.
The location of the hour hand is in 35 + x/12.




Now to solve the question, what time will the small and big hand meet past 7:
(35 + x/12) - x = 0
this means 11x/12 = 35.... x = 38.18
Time: 7:38.18 ... the two hands meet.



What time will they form a right angle: two times:
(35 + x/12) - x = ±15
positive right hand value:
11x/12 = 20 ... x = 21.82
Time: 7:21.82 ... the two hands form 90°, the minute hand did not pass the hour hand.

negative right hand value:
11x/12 = 50 ... x = 54.55
Time: 7:54.55 ... the two hands form 90°, the minute hand passed over the hour hand.


What time will they form 180°, minute hand will not pass the hour hand by this time.
(35 + x/12) - x = 30
11x/12 = 5 ... x = 5.45
Time: 7:05.45 ... the two hands form a straight line.


d:

Answer 2

The small and big hands meet at 12:00. It becomes a right triangle at 3:00 and 5:00, and 180 degrees at 6:00.

Answer 3

I assume you mean:

What is the first time after 7:00 when the hands of the clock form the various angles?

Let
r = rate of hour hand
12r = rate of minute hand
x = distance traveled by hour hand

1) When will the hands meet?

x + 7 = distance traveled by minute hand

time = distance/rate
time = x/r = (x + 7)/(12r)
12rx = r(x + 7)
12x = x + 7
11x = 7
x = 7/11 hours

Time = 7 7/11 ≈ 7:38:11
____________

2) When will the hands be at a right angle?

x + (7 - 3) = distance traveled by minute hand
x + 4 = distance traveled by minute hand

time = distance/rate
time = x/r = (x + 4)/(12r)
12rx = r(x + 4)
12x = x + 4
11x = 4
x = 4/11 hours

Time = 7 4/11 ≈ 7:21:49
____________

3) When will the hands be at 180°?

x + (7 - 6) = distance traveled by minute hand
x + 1 = distance traveled by minute hand

time = distance/rate
time = x/r = (x + 1)/(12r)
12rx = r(x + 1)
12x = x + 1
11x = 1
x = 1/11 hours

Time = 7 1/11 ≈ 7:05:27

Answer 4

The small hand (hour hand) moves 360 degrees in 12 hours, i.e., 30 degrees per hour or 1/2 degree per minute.

The big hand moves 360 degrees in 60 minutes, i.e., 6 degrees per minute.

At 12:00 both the hands are at 0 degrees. Therefore, at 7:00 hours big hand will be at 0 degree & small hand at 210 degrees. So the angle between them is 210 degrees.

For this to become 90 degrees, the angle should be reduced by 120 degrees. Every minute the reduction in angle is (6-1/2)=5.5 degrees. It will take
120/5.5 minutes to reduce the angle by 120 degrees i.e., to get 90 degrees.

Time for reduction of 120 degrees
=120/5.5=21 minutes 49.09 seconds

At 7:21:49.09, the hands will be at 90 degrees

Similarly to have an angle of 180 degrees, it should be reduced by 30 degrees from 210 degrees at 7:00

time required for reduction of 30 degrees=30/5.5
=5 minutes 27.27 sec.

At 7:05:27.27, the hands will be at 180 degrees.

Answer 5

Right angle at 3:00 & 9:00 and a bunch of other times, too.

180* at about 12:33, 11:26 and a bunch of other times.

When will th hands meet? 12:00, of course, and 6:32.

Answer 6

Your buddies are jumping the gun on this one.
At 7 PM, the big hand is at 0 deg and advances 360 degrees in one hour. The small hand is at 210 degrees and and advances 30 degrees in one hour. At some time (TM), they meet.
So 360*TM = 210+30*TM
and 330 TM = 210, so TM = 7/11 hour= 38.1818+ minutes after 7.

The same reasoning can be used to solve the other problems.

Answer 7

note
meet at 7:40

right angle 7:22

180 degrees 7:06

Answer 8

The hands of any clock meet once, they make angle of 180 degrees once and they make right angles twice in every hour.

After 7.00, the hands will make angle of 180 degrees at slightly ahead of 7.05, they will meet at slightly ahead of 7.37 and they will make right angles at slightly ahead of 7.21 and 7.54 (In one hour)