At what time between 2pm and 3pm is the 1st right angle formed
Answers
Answer:
2 o'clock plus 27.27 minutes
Given:
A right angle is formed between 2 pm and 3 pm.
To find:
The first right angle formed between the time 2 o'clock and 3 o'clock.
Solution:
Total degree in a click which is shaped like a circle: 360°
The number of degrees a minute hand will cover- 360 / 60 = 6°
The minutes the hands cover when right angle 90/ 6 = 15
This means when the hands are at a ninety-degree angle they are 15 minutes apart.
The number of degrees covered by the hour hand in an hour:
= 360 / 12
= 30°
The number of degrees covered by the hour hand in a minute:
= 360 / 12 × 60
= 0.5°
We have to start at 2:00, the time when the minute hand is at 0 degrees and the hour hand is at (360)*2/12 = 60 degrees.
We must find the time T it takes for the hour hand of the clock to move to an angle A(hour) at the same time that the minute hand is at an angle of
A(hour) + 90.
The minute hand rotates at 360 degree per hour
= (360 degree)/60 minutes
= 6 degree/minute
=0.1 s
The hour hand moves at 1/12th the speed of the second hand, so its rotational rate is
= 0.5 degrees/minute.
= 0.0083 degree/second)
So the angle A(minute) of the minute hand at any time t [ sec] will be A(m)
= 0.1 t.
The angle of the hour hand will be A(hour) = 60 + 0.0083 t.
60 degrees is added as the hour hand has a “head start” of 60 degrees at 2:00.
Now the task is to find the time t at which
A(m) = A(h) + 90
0.1 t = 60 + 0.0083 t + 90
This solves to give us the answer
= 1635.8 s
=27.26 m
= 27 min 15.6 sec
So the hour and minute hands will form a right angle at 2:27 pm
(2 hours 27 minutes 15.6 seconds)
Therefore the correct answer is 2:27 pm.