1

EDIT: Method $1$ is false, as pointed out by Hetebrij.

If it is night, how would one find the height of the building?

By assuming I am trying to find the height of a building at night, I am assuming that the building (or anything else) casts no shadow, so one cannot use similarities between triangles to find the height.

Also, assume that your only method of measurement is a ruler whose length is only $6.5$ meters and a clock.

Note that you cannot borrow (or steal) the blueprints for the building, and that all floors have different heights.

Here are several feasible methods that I have thought of.

$1.$ Using the Speed of a Elevator

This method assumes that there is one floor that is less than $6.5$ meters tall, and that there is a elevator.

Ride the elevator to see how long it takes to move $1$ floor. Say it took $a$ seconds. Then calculate the height of the room, which $h$m.

Ride the elevator from bottom to top. Say it took $b$ seconds. Then the height of the building would $\frac{b}{a} \times h$(m).

$2.$ Drop a ball from the Building

After calculating the time it takes for all ball to drop down of a building, use that $t=\sqrt{\frac{2h}{g}}$.

This assumes, of course, that there is no air resistance. Further methods concerning a falling body with air resistance are discussed here.

I cannot think of any other methods for finding the height of a transparent building. What are other methods that one can calculate it?

S.C.B.
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  • If you can measure angles then triangulation is a good idea – Renart Feb 10 '16 at 09:52
  • Triangulation allows you to measure the distance from a point on the ground to a top corner of the building. Then you measure the distance from that point on the ground to the bottom corner of the building and use pythagorean theorem. It'll work if your bulding is not invisible. – Renart Feb 10 '16 at 09:59
  • that's why you need triangulation to measure this distance – Renart Feb 10 '16 at 10:02
  • Please read about triangulation. You will understand more. @theonewhoaskedthisquestion – Win Vineeth Feb 10 '16 at 10:02
  • @$\Delta\alpha\mu o\nu$, if you want to get pinged, you should be having a username that people can type. Make it difficult for them, you don't get any sympathy when you reap the consequences yourself. – hmakholm left over Monica Feb 10 '16 at 10:10
  • OP, http://math.stackexchange.com/users/edit/current - the first editable field is your display name. – hmakholm left over Monica Feb 10 '16 at 10:12
  • Why the down-vote? – S.C.B. Feb 10 '16 at 10:14
  • The elevator idea won't work as you have to accelerate and decelerate. For one floor this is a huge portion of the time in the elevator. For all floors this is a small portion of the time in the elevator. – Hetebrij Feb 10 '16 at 10:15
  • @MXYMXY Well, I did upvote... which means 3 people surely down voted. Just correcting you, it's not "someone has" but "some people have". – Win Vineeth Feb 10 '16 at 10:16
  • @MXYMXY: You can't delete your own question now because it has upvoted answers. (And I don't think it is that bad either; I don't quite understand the downvotes). – hmakholm left over Monica Feb 10 '16 at 10:23
  • @Hetebrij Is this why my question was downvoted? – S.C.B. Feb 10 '16 at 10:51
  • @MXYMXY Don't know. It is just that the the elevator idea won't work. – Hetebrij Feb 10 '16 at 10:53

4 Answers4

3

I just want to point out that you can still use the similar triangles method, even though the building casts no shadow:

Just put your head to the ground $D$ and then position the upright measuring stick in a distance $|DC|$ from you such that the top of it $E$ coincides with the top of the building $A$, as seen from your perspective. Now measure the distance from your head to the stick $|DC|$, and then the distance from the stick to the building $|CB|$. Then you can find the height.

tria

Bobson Dugnutt
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3

Go to the top of the building, scream and use stopwatch to time for the echo off the ground.

orion
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2

You can take something, say a ball (or maybe something bigger for practical purposes) to the rooftop. It'll cast a shadow. Then, you can use the triangle rules to find the height. Not too smart, but works. ;)

MathIsNice1729
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    Nice hole you found in my conditions. I think that I am going to say that it is night, so you cannot see the shadow. But you should get a upvote for pointing that out. I am sorry. – S.C.B. Feb 10 '16 at 09:55
  • Then I cannot use any kind of torch or lighting instruments either, right? – MathIsNice1729 Feb 10 '16 at 10:02
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    Yes, that is a assumption. – S.C.B. Feb 10 '16 at 10:03
  • Well, you can bounce the ball and use the elasticity constant of the ground. Check after how many falls the maximum height the ball achieves is measurable. Measure it. And you're done. – MathIsNice1729 Feb 10 '16 at 10:12
1

Very hypothetical question, but here's my try- (i) Go to another building next to it whose height you know and each floor is uniform in height. Go to that point where you can see that you are flat with this transparent one. (ii) Go to the shop and exchange your scale for a protractor. Stand 30m from the building and measure the angle to the top. Repeat at 60m distance. From the two angle you can know. (iii) Exchange the scale and the clock for a barometer in the shop. take the barometer to the top. You will know from the pressure difference. (iv) Bribe the security guard of the building with the scale and clock and ask him the height.

Many more... Of course, all assume certain things like security guard should exist, there should be stairs in the building, shops nearby etc... but I hope these will suffice.

Win Vineeth
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  • An how are you going to measure the angle to the top? Your only method of measurement is a ruler and a timer. You cannot know the angle, which is also a unit of measurement. – S.C.B. Feb 10 '16 at 10:02
  • As I said, exchange the scale and clock for a protractor in the shop – Win Vineeth Feb 10 '16 at 10:03
  • Oh, I think you should space your answer a bit more. I try to read quickly, so I missed that part. Sorry. – S.C.B. Feb 10 '16 at 10:04
  • Well thank you. You also helped me with latex last time. Can you help me as to how to space my answers? I press enter but it never goes to the next line. – Win Vineeth Feb 10 '16 at 10:05
  • Use
    , or double enter.     – S.C.B. Feb 10 '16 at 10:08