Chapter 4.1, Problem 81E

Physics. An object dropped off the top of a tall building falls vertically with constant acceleration. If s is the distance of the object above the ground (in feet) $t$ seconds after its release, then $s$ and $t$ are related by an equation of the form $s=a+b{t}^2$ where $a$ and $b$ are constants. Suppose the object is $180$ feet above the ground 1 second after its release and $132$ feet above the ground $2$ seconds after its release.

(A) Find the constants $a\text{ and }b.$

(B) How tall is the building?

(C) How long does the object fall?