Between three o'clock and four o'clock, when does the minute hand and the hour hand on the clock coincide?
In fact, the coincidence of the hour hand and the minute hand is a deformed pursuit problem. Only the hour hand and the minute hand move on the circumference, and the speed of the hour hand and the minute hand is an angle.
As we know, the hour hand and the minute hand rotate 30 degrees and 360 degrees per hour respectively. At exactly three o'clock, the hour hand points to three o'clock, making 90 degrees with the minute hand.
The equivalent relationship of the pursuit problem is: the distance of the difference+the distance of the car (or person) in front = the distance of the pursuer.
Solution: let x hours pass after three o'clock, and the hour hand and the minute hand coincide for the first time.
Then it is: 90+30x = 360x.
When x=3/ 1 1 (hours) is solved, we can know when it coincides.
1, between 7 and 8 o'clock,
When do the hour hand and minute hand form a right angle?
Solution: Set it between 7 o'clock and 8 o'clock.
The minute hand and the minute hand are at right angles.
According to the meaning of the question:
=2 10-90
Solution:
Or: 7 o'clock between 7 o'clock and 8 o'clock.
The minute hand and the minute hand are at right angles.
According to the meaning of the question:
=2 10+90
Solution:
When does the hour hand and the minute hand coincide between 7 o'clock and 8 o'clock?
Solution: Set it between 7 o'clock and 8 o'clock.
The minute hand and the minute hand coincide, according to the meaning of the question:
=2 10
Solution:
3. When are the hour hand and the minute hand in a straight line?
Solution: Set it between 7 o'clock and 8 o'clock. At 7 o'clock, the hour hand and the minute hand are in a straight line. According to the meaning of the questions, they are listed as follows:
=2 10- 180
, solution: