Q. 5.19 - Intermediate Algebra

Question

The polynomial function $h\left(t\right)=-16t^2+150$ gives the height of a stone t seconds after it is dropped from a 150-foot tall cliff. Find the height after t = 0 seconds (the initial height of the object). 

Step-by-Step Solution

Answer

The height is 150 feet 

Step 1. Given information

The polynomial function for the height is

$h\left(t\right)=-16t^2+150$

Height of drop = 150 ft.

We have to find the height after t = 0 seconds.

Step 2. Substitute t=0 in h ( t )

$\begin{array}{l}\text{We have }h\left(t\right)=-16t^2+150\\ \text{At }t=0,\text{ we have}\\ \Rightarrow h\left(t\right)=-16{\left(0\right)}^2+150\\ =-16\left(0\right)+150\\ =150\end{array}$

Therefore, the initial height of the object is 150 ft.