A man stands 15m far in front of a large plane mirror. How far must he walk before he is 5m away from his image?10 m towards the mirror5 m away from the mirror12.5 m towards the mirrorNone of the above
Question
A man stands 15m far in front of a large plane mirror. How far must he walk before he is 5m away from his image?10 m towards the mirror5 m away from the mirror12.5 m towards the mirrorNone of the above
Solution
The answer is 10 m towards the mirror.
Here's the step-by-step explanation:
- The man is initially 15m away from the mirror.
- The image in a plane mirror is the same distance behind the mirror as the object is in front. So, the man's image is also 15m behind the mirror.
- The total distance between the man and his image is therefore 15m (man to mirror) + 15m (mirror to image) = 30m.
- If the man wants to be 5m away from his image, he needs to decrease this distance by 25m.
- Since the man and his image move towards each other at the same speed (because the image in a plane mirror "moves" as the object does), the man only needs to walk half this distance.
- So, the man must walk 25m / 2 = 12.5m towards the mirror.
So, the correct answer is "12.5 m towards the mirror".
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