How to Measure the Height of Your House ?

If I asked you to measure your height, what would you do?

Most folks would whip out a tape measure and stretch it from the ground to the tip of the head and read off the number given. But what if I asked you to measure the height of your house? Well maybe you would climb onto the roof, drop the tape measure to the ground, and repeat. But now, suppose I bring you to a hotel or a multi-story apartment or the world’s tallest building, the Bhurj Khalifa. What would you do?

The question described above is one of scalability. We want to find an algorithm to measure distance that is unaffected by the distance itself. Hopefully, you really thought about how to solve the problem, and maybe you came up with a solution or two, or maybe not. Either way, you probably realized that it’s a deceptively tricky question. Physics teachers love to ask new students about this question, partially because it takes creativity to find a suitable answer, and partially because the most clever solutions highlight the uniformity and beauty of nature’s laws. Without further ado, here’s five different ways to solve the problem:

1. Drop a ball from the top of the building and measure the time to hit the ground.

   1. Calculation: height in feet = 16.09 * (time in seconds)2

2. Standing back, measure the distance to the building, and the angle your eyesight makes

   1. Calculation: height in feet = tangent(angle) * horizontal distance in feet

3. Measure the shadow of an object with a known height and then that of the building

   1. Calculation: The ratio of the height of each over the shadow length is constant

4. Measure the air pressure at the top versus the bottom using the barometer on your phone

   1. Calculation: height in feet = change in pressure / (density of air times 16.09)

5. Pop a balloon at the top and measure the time it takes for a friend to hear it at the ground

   1. Calculation: height in feet = time * 343

Wow! Physicists deserve a lot more appreciation for creativity and ingenuity.

In the meantime, be sure to challenge your friends and family to come up with as many answers as possible!