Question

The polynomial function $h\left(t\right)=-16t^2+175$gives the height of a ball t seconds after it is dropped from a 175-foot tall bridge. Find the height after t = 3 seconds.

Short answer

The height is 31 feet.

Step-by-step solution

Step 1. Given information

The polynomial function for the height is

$h\left(t\right)=-16t^2+175$

Height of drop = 175 ft.

We have to find the height after t = 3 seconds.

Step 2. Substitute t=0 in h(t)

$\begin{array}{l}\text{Wehave}h\left(t\right)=-16t^2+175\\ \text{At}t=3,\text{wehave}\\ \Rightarrow h\left(t\right)=-16{\left(3\right)}^2+175\\ =-16\left(9\right)+175\\ =-144+175\\ =31\end{array}$

Thus, the height after t=3 seconds is 31 ft.