What are the initial positions of the two hands, and at what angular speed in degrees per hour do the two hands move?
How would I go about figuring this out?
Mario was studying angles and wondered if during his math class the minute and hour hands of the clock formed a right angle. If his class meets from 6:00 P.M. to 6:50 P.M., is a right angle formed? If so, figure out to the nearest second when the hands form the right angle.
Hello, stallioncane!
Here is my approach to Clock-hands Problems.
Mario was studying angles and wondered if during his math class
the minute and hour hands of the clock formed a right angle.
If his class meets from 6:00 P.M. to 6:50 P.M., is a right angle formed?
If so, figure out to the nearest second when the hands form a right angle.
You might think that one answer looks like this:
But this is incorrect.Code:* * * * * * * * * * * * *-------- * 3 * | * | * | * * * * * * * * 6
By the time the minute hand has moved 90^{o} to the "3",
. . the hour hand has already moved toward the "7".
The minute hand moves 360^{o} in 60 minutes.
It moves per minute.
It starts at "12" (0^{o}) and in the next minutes, it move degrees.
The position of the minute hand at time is: . degrees.
The hour hand moves 30^{o} in 60 minutes.
It move per minute.
It starts at "6" (180^{o}) and in the next minutes, it moves degrees.
The position on the hour hand at time is: . degrees.
There are two possible cases.
[1] The hour hand is 90^{o} ahead of the minute hand: .
. . .
. . .
Time: 16 minutes, 22 seconds after 6 o'clock.
[2] The minute hand is 90^{o} ahead of the hour hand: .
. . .
. . .
Time: 49 minutes, 5 seconds after 6 o'clock.