A package is dropped from a helicopter at 1600 feet. The height of the package can be modeled by:


h = -16t squared + 1600 , where h is the height of the package in feet and t is the time in seconds.

How long will it take for the package to hit the ground?

10

To determine how long it will take for the package to hit the ground, we need to find the value of t when the height of the package, h, is equal to 0.

Given the equation h = -16t² + 1600, we substitute h = 0 and solve for t:

0 = -16t² + 1600

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, it is easier to use the quadratic formula:

t = (-b ± √(b² - 4ac)) / (2a)

Using the equation -16t² + 1600 = 0, we can see that a = -16, b = 0, and c = 1600. Plugging these values into the quadratic formula, we get:

t = (0 ± √(0² - 4(-16)(1600))) / (2(-16))
t = (0 ± √(0 + 102400)) / (-32)
t = (0 ± 320) / (-32)

Simplifying further, we have two possible solutions:

t₁ = (0 + 320) / (-32) = 320 / -32 = -10
t₂ = (0 - 320) / (-32) = -320 / -32 = 10

Since time cannot be negative in this context, we discard the negative solution.

Therefore, it will take 10 seconds for the package to hit the ground.