Finding the height of a Building at Night

Question

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?

Answer 1

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. ;)

Answer 2

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.

Answer 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.

Answer 4

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