Answer :
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
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