Question

A relief package is released from a helicopter at 1600 feet. the height of the package can be modeled by the equation: h = -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. a. write the equation that you are trying to solve. b. solve the equation by factoring.

Answer 1

The equation to solve is 0 = -16t^2 + 1600. By factoring t^2 - 100 = 0, we determine that the package will hit the ground after 10 seconds.

Step-by-step explanation:

Solving Quadratic Equations by Factoring

The question involves solving a quadratic equation to find out the time it takes for a relief package released from a helicopter to hit the ground. The given quadratic equation is h = -16t^2 + 1600, where h is the height in feet and t is the time in seconds.

Part A: Write the equation to solve

To find when the package hits the ground, we set h to 0 because the height at ground level is 0 feet. Therefore, the equation we are solving is 0 = -16t^2 + 1600.

Part B: Solving by Factoring

First, we can divide both sides of the equation by -16 to simplify:

0 = t^2 - 100

We then factor the right-hand side:

0 = (t - 10)(t + 10)

Setting each factor equal to zero gives us two possible solutions for t:
t - 10 = 0 or t + 10 = 0, which means t = 10 seconds or t = -10 seconds. Since time cannot be negative, we discard the -10, and the package will hit the ground after 10 seconds.