Question

17. A firefighter is on the fifth floor of an office building. She needs to throw a

rope into the window above her on the seventh floor. The function
h=-16t² + 36t models how high above her she is able to throw the rope.
If she needs to throw the rope 40 feet above her to reach the seventh-floor
window, will the rope get to the window? Show your work.
17

Answer 1

Explanation:

To determine whether the rope will reach the seventh-floor window, we need to find the value of 't' when the height above her, represented by the function h = -16t² + 36t, is equal to 40 feet.

Setting h = 40, we have:

40 = -16t² + 36t

To solve this quadratic equation, we can rearrange it to:

16t² - 36t + 40 = 0

However, upon solving this equation, we find that it does not have any real solutions. This means that there is no value of 't' for which the height above her will be exactly 40 feet. Therefore, the rope will not reach the seventh-floor window, as she needs to throw it 40 feet above her.