A relief package is released from a helicopter at 1600 feet. The height of the package can be modeled by the equation

h(t)= -16t^2+1600
where h is the height of the package in feet and t is the time in seconds. The pilot wants to know how long it will take for the package to hit the ground. Write the equation that you are trying to solve (hint - what would be the height, h(t), of a package ON THE GROUND?) then solve the equation using whichever method you are comfortable with. Be sure to show your work using the equation editor.

10, been there, done that

To find the time it will take for the package to hit the ground, we need to solve the equation h(t)=0, since the height of the package on the ground is zero.

The given equation is h(t) = -16t^2 + 1600.

So, we need to solve the equation -16t^2 + 1600 = 0.

To solve this equation, we can use the quadratic formula, which is:

t = (-b ± √(b^2 - 4ac)) / 2a

Comparing this with our equation -16t^2 + 1600 = 0, we can identify the values of a, b, and c:
a = -16
b = 0 (since there is no t-term)
c = 1600

Now, we can substitute these values into the quadratic formula and solve for t:

t = (-0 ± √(0^2 - 4(-16)(1600))) / (2(-16))
= (√(0 + 102400)) / (-32)
= (√102400) / (-32)
= (√102400) / -32

Since we want to find the time it will take for the package to hit the ground, we only consider the positive square root, so

t = √102400 / -32

Now, we can simplify the expression:

t = -(√(256 * 400)) / 32
= -(16 * √400) / 32
= -(16 * 20) / 32
= -320 / 32
= -10

So, the time it will take for the package to hit the ground is 10 seconds.