a bullet is fired into the air with an initial upward velocity of 64 fps from the top of a building 80 feet high. The equation that gives the height of the bullet at any time (t), is h=80+64t-16t^2. Find the times at which the arrow will be 128 feet in the air? This talks about a bullet but asks about an arrow, how do I answer this for the arrow?

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t^2-4t-5=-8

t^2-4t-5=-8

(t-1)(t-3)=0

Step 1: h = -16t^2+64t+80=128.

To answer the question, let's start by understanding the equation given for the height of the bullet at any time (t): h = 80 + 64t - 16t^2.

The equation represents a quadratic function, where h represents the height of the bullet at time t. We need to find the values of t for which the height of the bullet is 128 feet.

Substitute the value of h = 128 into the equation: 128 = 80 + 64t - 16t^2.

Now, we need to solve this quadratic equation to find the values of t that satisfy the equation.

Rearranging the equation, we get: -16t^2 + 64t + 48 = 0.

To solve this quadratic equation, we can use various methods, such as factoring, completing the square, or using the quadratic formula. Let's apply the quadratic formula:

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / 2a.

In our equation, a = -16, b = 64, and c = 48. Substituting these values into the quadratic formula, we have:

t = (-64 ± √(64^2 - 4(-16)(48))) / (2(-16)).

Simplifying this expression further:

t = (-64 ± √(4096 + 3072)) / (-32).

t = (-64 ± √(7168)) / (-32).

Next, we calculate the square root of 7168, which is approximately 84.85:

t = (-64 ± 84.85) / (-32).

Now we have two possible solutions:

1. t = (-64 + 84.85) / (-32) ≈ 0.91 seconds.
2. t = (-64 - 84.85) / (-32) ≈ 4.75 seconds.

Therefore, the bullet (or arrow) will be 128 feet in the air at approximately 0.91 seconds and 4.75 seconds after it is fired.

Keep in mind that we assumed the equation for the bullet's height is the same as for the arrow in this particular question.