# Building Height Calculated - Thanks Thaakisfox!

• TeenieWeenie
In summary, the problem of calculating the height of a building based on the horizontal distance a ball travels when thrown at a velocity of 2.2 m/s has been solved. The formula used was h(t) = Vo*t + 1/2 at^2 and after plugging in the given values, the height was determined to be approximately 1311.48 meters.
TeenieWeenie
Problem solved! Thanks again Thaakisfox!

## Homework Statement

A ball thrown horizontally at 2.2 m/s from the roof of a building lands 36 m from the base of the building. Calculate the height of the building.
Vox = 2.2 m/s
Xo = 0m
Vx = 0 m/s
X = 36m

## Homework Equations

y = Vosin ao - (0.5)(g)(t^2)

## The Attempt at a Solution

I tried plugging it in but then I have a missing time...?

Last edited:
This is a horizontal projection hence you don't need any sine etc. Just calculate the time of descent from the velocity and horizontal displacement by dividing them. And then the vertical component is simple freefall.

I'm kinda confused.
What formula would I use then?

x=Vo *CosAo * t

No. It is a horizontal projection. You don't need any of those sine or cosine function.

You throw the ball with horizontal velocity Vo. Since it has no acceleration in the horizontal direction, the distance it travels is simply: x=Vo*t where x is given (the distance from the base of the building). from here you can get t. Now in the vertical plane it is just simple freefall, so use the formula which gives the distance when freefall takes place

36 m = 2.2 m/s * t

36/2.2 s = t
16.36 s = t

h(16.36) = 0*t + (0.5)(-9.8m/s^2)(16.36^2)
= -1311.48304 m ?

I think something went wrong... :(

The calculation is correct. The given data seem insensible.

Insensible?

That happens many times in textbooks, that the given data for a problem don't make sense. For example there probably arent many buildings taller than 1km, and especially someone throwing a ball off.
But your calculation is correct. (That minus sign doesn't matter, it just means that you took the y-axis to point upwards, and that's why the acceleration has a negative sign. But you are searching for the absolute value of the height anyway, so just take that minus sign away.)

Oh! Good observation.

Problem solved! Thanks again Thaakisfox!

## What is building height calculated?

Building height calculated is a method used to determine the height of a building by measuring the distance from the ground to the highest point of the structure.

## Why is building height calculated important?

Building height is an important factor in urban planning and construction as it affects the structural integrity, safety, and aesthetic appeal of a building. It also has implications for zoning regulations and building codes.

## How is building height calculated?

Building height is typically calculated using a variety of methods such as trigonometry, laser technology, and photogrammetry. These methods involve measuring the angles and distances of a building from different vantage points and using mathematical equations to determine its height.

## What are the factors that affect building height calculation?

The factors that affect building height calculation include the elevation of the site, the slope of the land, the height of neighboring buildings, and any obstructions such as trees or power lines that may impact the measurement.

## Are there any limitations to building height calculation?

Yes, there can be limitations to building height calculation depending on the method used. Factors such as weather conditions, equipment limitations, and the complexity of the building's design can affect the accuracy of the measurement. It is important to use multiple methods and take into account any potential errors to ensure an accurate calculation.

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