pam is visiting a historic town with an old - fashioned water well in the town square. she drops a pebble…

pam is visiting a historic town with an old - fashioned water well in the town square. she drops a pebble into the well from a height of 27 feet above the surface of the water. to the nearest tenth of a second, how long does it take for the pebble to hit the water? hint: use the formula h = - 16t² + s.

pam is visiting a historic town with an old - fashioned water well in the town square. she drops a pebble into the well from a height of 27 feet above the surface of the water. to the nearest tenth of a second, how long does it take for the pebble to hit the water? hint: use the formula h = - 16t² + s.

Answer

Explanation:

Step1: Identify values for formula

We know that when the pebble hits the water, $h = 0$ and the initial height $s=27$. The formula is $h=-16t^{2}+s$. Substituting the values, we get $0 = - 16t^{2}+27$.

Step2: Rearrange the equation

Rearrange $0=-16t^{2}+27$ to solve for $t^{2}$. We have $16t^{2}=27$. Then $t^{2}=\frac{27}{16}$.

Step3: Solve for t

Take the square - root of both sides. Since $t>0$ (time cannot be negative in this context), $t=\sqrt{\frac{27}{16}}=\frac{\sqrt{27}}{4}=\frac{3\sqrt{3}}{4}\approx\frac{3\times1.732}{4}=\frac{5.196}{4}=1.3$.

Answer:

$1.3$