Question

A clock hang on the wall is facing a plane mirror hanged on the opposite wall. As you see the reflection of
the clock on the mirror, the clock shows the time of 9:00. What is the real time?
A 2:00
B. 3:00
C.4:00
D. 5:00
how far away is the man's image from the mirror?​

Answer 1

Answer:

B. 3:00

As the mirror is plane.

So, distance of image of man = distance of man from mirror

But image will be in opposite direction.

Explanation:

Answer 2

Correct answer is (A)2:00.

• If the reflection of the clock in the mirror shows the time of 9:00, then the hour hand and minute hand of the reflected clock will point to the "9" and "12" respectively.
  
  
• The angle between the hour hand and the minute hand of a clock at 9:00 is 120 degrees. However, the angle between the hour hand and minute hand of the reflected clock is twice the actual angle between them because the reflected image appears to be behind the mirror. Therefore, the angle between the hour hand and minute hand of the actual clock is 60 degrees.
  
• We know that the hour hand moves 0.5 degrees per minute, and the minute hand moves 6 degrees per minute. Therefore, to find out the real time when the angle between the hour and minute hand is 60 degrees, we can use the following formula:
  
  0.5x + 6y = 60
• Where x is the number of minutes past the hour, and y is the number of minutes past 12. Solving this equation, we get x = 120 and y = 5. Therefore, the real time is 2:05, which is option A.
• To find out how far away the man's image is from the mirror, we need to use the law of reflection, which states that the angle of incidence is equal to the angle of reflection. Since the man is standing in front of the mirror, his image is behind the mirror. Therefore, we need to consider the angle between the man's eye level and the mirror.
  
• Let's assume that the man's eye level is 5 feet from the ground, and the mirror is 6 feet tall. Therefore, the angle of incidence is:
  
  arctan(5/6) = 40.6 degrees
  
• According to the law of reflection, the angle of reflection is also 40.6 degrees. Therefore, the man's image is located 5 feet away from the mirror, at an angle of 40.6 degrees.

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