PROBLEM $3[20$ marks$]$

High$-$rise buildings $($Fig $2.)$ can be idealized as a cantilever beam, and the

following function can model wind force on the building.

$f(z)=100+4(\frac{Z}{H}{)}^{\frac{1}{2}}$

where:

$z=$ the elevation above the ground $($m$)$

$H=$ the height of the building $(=100m).$

a$.$ Numerically evaluate the total wind force $F$ exerted at the

base of the building by integrating the force function over

the building height.

$F={\displaystyle \underset{0}{\overset{H}{}}}f(z)dz$

Use the Adaptive Quadrature or Richardson

Extrapolation to compute $F$ using two estimates from

$n=2$ and $n=4.$ Choose the best method that suits the

problem. Justify your choice. Use hand calculation and

Fig $2.$ High$-$rise

building

show all the steps. $[18]$

b$.$ Discuss two potential sources of error associated with numerical integration.

$[2]$