For a experiment in physics class, a water balloon is dropped from the window of the school building. the window is 40 feet high. how long does it take until the balloon hits the ground? round to the nearest hundreth.

It takes 1.58 seconds.

The equation to represent this is of the form h(t) = -16t²+v₀t+h₀, where -16 is the gravitational constant, v₀ is the initial velocity, and h₀ is the initial height.  We do not have an initial velocity, since the balloon is dropped.  The initial height is 40.  This gives us the function
h(t) = -16t² + 40.

We will set this equal to 0:
0 = -16t² + 40

Subtract 40 from both sides:
0-40 = -16t² + 40 - 40
-40 = -16t²

Divide both sides by -16:
-40/-16 = -16t²/-16
2.5 = t²

Take the square root of both sides:
√2.5 = √t²
1.58 = t