Q.68 - Intermediate Algebra

Question

A girl is throwing a ball off the cliff into the ocean. The polynomial

$h\left(t\right) = -16t^2 + 200$ gives the height of a ball $t$ seconds after it is dropped from a $250$-foot tall cliff. Find the height after $t=3$ seconds.

Step-by-Step Solution

Answer

The height after $t=3$ seconds is $56$.

Step 1. Given Information

The given polynomial function $h\left(t\right) = -16t^2 + 200$ gives the height of a ball $t$ seconds after it is dropped from a $250$-foot tall cliff.

We find the height after $t=3$ seconds.

Step 2. The given polynomial function is h ( t )   =   − 16 t 2   +   200

The function is $h\left(t\right) = -16t^2 + 200$

putting $t=3$

$$\begin{gathered} h\left(3\right) = -16{\left(3\right)}^2 + 200 \\ h\left(3\right) = -16\times 9+ 200 \\ h\left(3\right) = -144 + 200 \\ h\left(3\right) = 56 \end{gathered}$$