Question

A water balloon is dropped from a height of 16 feet. The function h=-16x^2+16 gives the height h of the balloon after x seconds. When does it hit the ground?

Answer 1

The ballon will hit the ground after 1 s.

Explanation:

In this case we want to solve for x, but were given a equation to the height of the ballon, we can organize it in a way that isolates x on the left side of the equation so it can be used to what we want. So we have:

h = -16x^2 +16

h + 16x^2 = 16

16x^2 = 16 - h

x^2 = (16 - h)/16

x = sqrt(16 - h)/sqrt(16) = sqrt(16 - h)/4

When the ballon hits the ground it's height is 0 feet, so we substitute that on our equation and we'll have the right answer.

x = sqrt(16 - 0)/4 = sqrt(16)/4 = 4/4 = 1 s