Question

Benjamin threw a rock straight up from a cliff that was 72 ft above the water. If the height of the rock​ h, in​ feet, after t seconds is given by the equation nbsp h equals negative 16 t squared plus 84 t plus 72​, how long will it take for the rock to hit the​ water?

Answer 1

It will take 6 seconds for the rock to hit the​ water.

Explanation

The given equation is:  $h= -16t^2+84t+72$ , where $h$ is the height of the rock above the water after $t$ seconds.

When the rock will hit the water, then height of the rock will become zero. So we will plug $h=0$ into the above equation and then solve for $t$

So......

$-16t^2 +84t+72=0\\ \\ -4(4t^2-21t-18)=0\\ \\ -4(4t^2-24t+3t-18)=0\\ \\ -4[4t(t-6)+3(t-6)]=0\\ \\ -4(t-6)(4t+3)=0$

Now using zero-product property, we will get....

$t-6=0\\ t=6\\ \\ and \\ \\ 4t+3=0\\ 4t=-3\\ t= -\frac{3}{4}$

(Negative value is ignored as time can't be in negative)

So, it will take 6 seconds for the rock to hit the​ water.