Originally Posted by

**Soroban** Hello, sologuitar!

We are expected to be familiar with this formula: .$\displaystyle h \:=\:200t - 16t^2$

. . where $\displaystyle h$ is the height of the rocket (in feet) $\displaystyle t$ seconds after liftoff.

When is $\displaystyle h \,=\,400$ ?

We have: .$\displaystyle 200t - 16t^2 \:=\:400 \quad\Rightarrow\quad 2t^2 - 25t + 50 \:=\:0$

. . which factors: .$\displaystyle (2t-5)(t-10) \:=\:0$

. . and has roots: .$\displaystyle t \:=\:\tfrac{5}{2},\:10$

The fireworks will be detonated $\displaystyle 2\tfrac{1}{2}$ seconds after liftoff.