Question

A water fountain jet shoots short spurts of water over a walkway. The water spurts reach a maximum​ height, then come down into a pond of water on the other side of the walkway. The height above the​ jet, h, of a spurt of water t seconds after leaving the jet can be found by the function ​h(t)equalsminus16tsquaredplus16t. Find the time it takes for the spurt of water to return to the​ jet's height; that​ is, when ​h(t)equals0.

Answer 1

The spurt of water takes 1 second to return to the​ jet's height.

Step-by-step explanation:

The height above the​ jet, h, of a spurt of water t seconds after leaving the jet can be given by the function ​as follows :

`h(t)=-16t^2+16t` .......(1)

We need to find the time it takes for the spurt of water to return to the​ jet's height i.e. when h(t) = 0

Equation (1) becomes :

`h(t)=0\\\\-16t^2+16t=0\\\\16t(-t+1)=0\\\\t=0,t=1`

So, the spurt of water takes 1 second to return to the​ jet's height.