Building Height Calculated - Thanks Thaakisfox!

[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 = V_osin a_o - (0.5)(g)(t^2)

The Attempt at a Solution

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

 

[Thaakisfox]

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.

 

[TeenieWeenie]

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

x=Vo *CosAo * t

 

[Thaakisfox]

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

 

[TeenieWeenie]

36 m = 2.2 m/s * t

36/2.2 s = t
16.36 s = t

Formula for free fall: h(t) = Vo*t + 1/2 at^2
h(16.36) = 0*t + (0.5)(-9.8m/s^2)(16.36^2)
= -1311.48304 m ?

I think something went wrong... :(

 

[Thaakisfox]

The calculation is correct. The given data seem insensible.

 

[TeenieWeenie]

Insensible?

 

[Thaakisfox]

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.)

 

[TeenieWeenie]

Oh! Good observation.

Problem solved! Thanks again Thaakisfox!