A firefighter is on the fifth floor of an office building. She needs to throw a rope into the wiindow above her on the seventh floor. The function h=-16t^2+36t models how high above her she is able to throw a rope. If she needs to throw the rope 40 ft above her to reach the seventh-floor window, will the rope get to the window?

Question

A firefighter is on the fifth floor of an office building. She needs to throw a rope into the wiindow above her on the seventh floor. The function h=-16t^2+36t models how high above her she is able to throw a rope. If she needs to throw the rope 40 ft above her to reach the seventh-floor window, will the rope get to the window?

I don't know where to plug each number in the equation.

Answer 1

I assume h = height = 40 feet. Whatever t stands for, I assume that is the value you are trying to find. Will it also be expressed in units of feet? If so, this leads me to:

16t^2 + 36t - 40 = 0

4(4t^2 + 9t -10) = 0

Unfortunately, I am unable to factor it any further. Are there any typos in your formula?

Sorry that I can't be of more help. Thanks for asking.

Answer 2

To determine if the rope will reach the seventh-floor window, we need to find the value of t when h = 40 ft. We can plug the given value of h = 40 into the equation h = -16t^2 + 36t and solve for t.

First, replace h with 40 in the equation:
40 = -16t^2 + 36t

Now, we have a quadratic equation. To solve this equation, we can set it equal to zero by subtracting 40 from both sides:
-16t^2 + 36t - 40 = 0

At this point, we can either factor the quadratic or use the quadratic formula. Let's factor it:
-4(4t^2 - 9t + 10) = 0

Now, we need to find two numbers that multiply to give 10 and add up to -9. The numbers are -4 and -5, so we can factor the quadratic equation further:
-4(2t - 5)(2t - 2) = 0

Now, we can set each factor equal to zero and solve for t:
2t - 5 = 0 or 2t - 2 = 0

Solving these equations, we find:
2t = 5 -> t = 5/2 = 2.5
2t = 2 -> t = 2/2 = 1

Now, we have two possible values for t: t = 2.5 and t = 1. We need to determine which one represents the time it takes for the rope to reach a height of 40 ft.

Substitute each value of t back into the original equation h = -16t^2 + 36t:
h = -16(2.5)^2 + 36(2.5) -> h ≈ 30 ft
h = -16(1)^2 + 36(1) -> h ≈ 20 ft

From the calculations, we can see that neither t = 2.5 nor t = 1 gives us a height of h = 40 ft. Therefore, the rope will not reach the seventh-floor window when it needs to be thrown 40 ft above the firefighter on the fifth floor.

Answer 3

To determine if the rope will reach the seventh-floor window, we need to plug in the given information into the equation and calculate the height at that time.

The equation given is h = -16t^2 + 36t, where h represents the height and t represents the time in seconds.

We want to find out if the height at time t is equal to or greater than 40 ft. So, we plug in h = 40 into the equation:

40 = -16t^2 + 36t

Now, we need to solve this quadratic equation to find the possible values of t. To do this, we rearrange the equation to make it equal to zero:

16t^2 - 36t + 40 = 0

We can then use the quadratic formula to solve for t:

t = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 16, b = -36, and c = 40. Plugging these values into the formula:

t = (-(-36) ± √((-36)^2 - 4(16)(40))) / (2(16))

Simplifying further:

t = (36 ± √(1296 - 2560)) / 32
t = (36 ± √(-1264)) / 32

Since the term under the square root is negative, we can conclude that there are no real solutions for t. This means that the rope will not reach the seventh-floor window if she needs to throw it 40 ft above her.