T-Shirt Quadratic

Algebra and a T-shirt cannon

Question:

The height \(h(t)\), in feet, of an airborne tee shirt t seconds after being launched can be approximated by \[h(t)=-15t^2+120t+10, 0\leq t\leq10\] find the times when the teeshirt will reach a fan at \(115\) feet above ground

Answer:

\[h(t) = -15t^2+120t+10\] You're looking for when \(h(t) = 115\), because that's when it will reach a fan. \[\begin{align} h(t) &= 115 \\[8pt]-15t^2+120t+10 &= 115 \end{align}\] rearrange and solve quadratic: \[\begin{align} 0 &= 115 - 10 - 120t + 15t^2 \\0 &= 105 - 120t + 15t^2 \\0 &= 7 - 8t + t^2 \\0 &= (t - 7)(t - 1) \\t &= 1 \hspace{6pt}\text{or } 7 \end{align}\]

Graph of curve h(t)