An old fashion clock with twelve numbers on the face and hands forms a right angle at 3:00. What is the next time they form a right angle?
I need work to be shown.
Clock Math Problem?
2020-08-10 10:49 pm
回答 (2)
2020-08-10 11:27 pm
✔ 最佳答案
Let y min after 3:00 be the next time when the two hands form a right angle.The hour hand turns 360°/12 = 30° in 60 min. Hence, in y min it turns 30° × (y/60) = 0.5y°
The minute hand turns 360° in 60 min. Hence, in y min it turns 360° × (y/60) = 6y°
When next time the two hands form a right angle, the minutes hand turns 180° more than hour hand:
6y = 0.5y + 180
5.5y = 180
y = 32 and 8/11
Answer: The time is (32 and 8/11) min ≈ 32.73 min after 3:00.
2020-08-10 11:25 pm
Hour hand:
makes one revolution in 12 hours
in one minute the angles increases by
360 / (12*60) = 0.5º
It starts at 3:00 which is 90º
ϴ₁ = 90 + 0.5m
----------------------
Minute hand
makes one revoulution in 1 hour
in one minute the angles increases by
360 / 60 = 6º
It starts at 0º
ϴ₂ = 6m
---------------------
The next time they will be at 90º
ϴ₂ - ϴ₁ = 90
6m - (90 + 0.5m) = 90
5.5m = 180
m = 32.7272727273
32 minutes 43.63... seconds
time will be
~ 3:32:44 <–––––––
makes one revolution in 12 hours
in one minute the angles increases by
360 / (12*60) = 0.5º
It starts at 3:00 which is 90º
ϴ₁ = 90 + 0.5m
----------------------
Minute hand
makes one revoulution in 1 hour
in one minute the angles increases by
360 / 60 = 6º
It starts at 0º
ϴ₂ = 6m
---------------------
The next time they will be at 90º
ϴ₂ - ϴ₁ = 90
6m - (90 + 0.5m) = 90
5.5m = 180
m = 32.7272727273
32 minutes 43.63... seconds
time will be
~ 3:32:44 <–––––––
收錄日期: 2021-04-24 07:57:19
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