[Guest]

A man is 6 feet tall. His wife is 5 feet tall and his two children are 4 feet and 3 feet. He wants to buy a flat mirror to place on a wall so that he and his family can stand in front of it and everyone can see themselves (their whole body) and everyone else at the same time. What is the minimum height of the mirror he should buy?

(Assume a persons eyes are at the top of their body)

Edited June 4, 2009 by psychic_mind

[Pickett]

A man is 6 feet tall. His wife is 5 feet tall and his two children are 4 feet and 3 feet. He wants to buy a flat mirror to place on a wall so that he and his family can stand in front of it and everyone can see themselves (their whole body) and everyone else at the same time. What is the minimum height of the mirror he should buy?

(Assume a persons eyes are at the top of their body)

Do we have any indication as to how far away they all will be standing? or is that up to us to decide the optimum for this problem? And along those lines, do they have to be standing together? or can they all be standing at different distances from the mirror?

[Guest]

4.5 feet mirror is required. It should be placed on the wall leaving 1.5 feet gap on the ground.

[Guest]

4.5 feet mirror is required. It should be placed on the wall leaving 1.5 feet gap on the ground.

How did you figure that? I was thinking similarily, but like this:

4 ft. - 1 foot off the ground - and Daddy needs to stand back a little more than the Kiddies and wife. This is assuming relatively "normal" room dimensions - you can make it smaller, but then they would need to have a bigger room - and so on.

[Guest]

4.5 mts ... at a height of 1.5 mts ..

The 6m guy shoulkd be able to see his head... so hang it at a height of 6m ... Now the smallest guy (3m) should be able to see his feet. Drawing the diagram would make it clear that the mirror should extend at least till half his height i.e. 1.5 mts

So, now 6-1.5 = 4.5 mts

[Guest]

I think that it doesn't matter how far they are from the mirror ... the minimum required wouldn't change

[Guest]

How did you figure that? I was thinking similarily, but like this:

4 ft. - 1 foot off the ground - and Daddy needs to stand back a little more than the Kiddies and wife. This is assuming relatively "normal" room dimensions - you can make it smaller, but then they would need to have a bigger room - and so on.

6 feet man needs a mirror at 6 feet from ground to see his head.

3 feet child needs a mirror at 1.5 feet from ground to see his feet.

So 6-1.5=4.5 feet mirror is needed and enough.

[Guest]

A man is 6 feet tall. His wife is 5 feet tall and his two children are 4 feet and 3 feet. He wants to buy a flat mirror to place on a wall so that he and his family can stand in front of it and everyone can see themselves (their whole body) and everyone else at the same time. What is the minimum height of the mirror he should buy?

(Assume a persons eyes are at the top of their body)

There are 3 answers for this, see the spoiler for explination, and the bottom has the three answers.

Due to the physics of mirrors one only needs a mirror half of thier height to see themselves in it at any distance, if the mirror didn't move then the height needed would be the tallest heigt - 1/2 of the small est heigt or 4.5 feet for every one to see themselves in the mirror completely, but if the mirror was not mounted on the wall and could move then the mirror would only need to be 3 feet for every one to be able to see themselves in the mirror. In order for every one to see each other in a flat mirror, that function is dependent on distance away from the mirror of both, and the only mirror that would be able to do that is if it touched the floor, or 6 feet because someone could stand right up against the mirror so people far away would need to look closer and closer to the floor and as the person gets further away from the mirror then the mirror needs to get closer to the floor, and to the point where it would be close enough to be considered touching the floor and the tallest needs to see himself in the mirror so the mirror needs to reach up to 6 feet. Though if it ment for the people to see each other when standing next to each other then it is the same as the first solution of tallest height - 1/2 of the smallest height, which would allow the tallest to see themselves, and for the smallest to see themselves.

The awnsers are 3 feet for a moveable mirror, 4.5 feet for a mirror mounted 1.5 feet above the floor, and a 6 foot mirror in the case of seeing every one at any point in the room to see each other.

Edited June 4, 2009 by tkn

[Guest]

the person who is tallest in the family is the man and he is 5 ft.

if we assume that the family stands in the centre of the room, then the maximum height of the mirror should be 2.5ft with the mirror standing at 2.5ft above ground. this is a numerical problem of reflection of light.

Edited June 4, 2009 by Satish.S

[Guest]

What about a two foot car mirrors like the ones that say "objects may be closer than they appear". They all should be able to fit in the mirror.

[Guest]

I'm sure someone around here will know the formulae behind this (I can't remember them

), but a flat mirror resting on the ground at an angle is able to display things much taller than its actual height (you know, like mirrors in shoe shops)... sorry I'm not providing any answer, just hinting in a general direction...

[Guest]

1'6" from the ground, and the mirror needs to be 4'6" in length.

[Guest]

There are 3 answers for this, see the spoiler for explination, and the bottom has the three answers.

Due to the physics of mirrors one only needs a mirror half of thier height to see themselves in it at any distance, if the mirror didn't move then the height needed would be the tallest heigt - 1/2 of the small est heigt or 4.5 feet for every one to see themselves in the mirror completely, but if the mirror was not mounted on the wall and could move then the mirror would only need to be 3 feet for every one to be able to see themselves in the mirror. In order for every one to see each other in a flat mirror, that function is dependent on distance away from the mirror of both, and the only mirror that would be able to do that is if it touched the floor, or 6 feet because someone could stand right up against the mirror so people far away would need to look closer and closer to the floor and as the person gets further away from the mirror then the mirror needs to get closer to the floor, and to the point where it would be close enough to be considered touching the floor and the tallest needs to see himself in the mirror so the mirror needs to reach up to 6 feet. Though if it ment for the people to see each other when standing next to each other then it is the same as the first solution of tallest height - 1/2 of the smallest height, which would allow the tallest to see themselves, and for the smallest to see themselves.

The awnsers are 3 feet for a moveable mirror, 4.5 feet for a mirror mounted 1.5 feet above the floor, and a 6 foot mirror in the case of seeing every one at any point in the room to see each other.

If they were standing right up against the mirror, would this still be the correct answers?

[Guest]

If they were standing right up against the mirror, would this still be the correct answers?

yes the answers work, due to the properties of plane mirrors. if you would like i could up load an image depicting why.