Q.67 - Intermediate Algebra

Question

A painter drops a brush from a platform $75$ feet high. The polynomial function $h\left(t\right) = -16t^2+ 75$ gives the height of the brush $t$ seconds after it was dropped. Find the height after $t=2$ seconds.

Step-by-Step Solution

Answer

The height after $t=2$ seconds is $11$.

Step 1. Given Information

A painter drops a brush from a platform $75$ feet high. The given function is $h\left(t\right) = -16t^2+ 75$ gives the height of the brush $t$ seconds after it was dropped.

We find the height after $t=2$ seconds.

Step 2. The given polynomial function is h ( t )   =   − 16 t 2 +   75

The function is $h\left(t\right) = -16t^2+ 75$

putting $t=2$

$$\begin{gathered} h\left(2\right) = -16{\left(2\right)}^2+ 75 \\ h\left(2\right) = -16\times 4+ 75 \\ h\left(2\right) =-64+75 \\ h\left(2\right) =11 \end{gathered}$$