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forsale [732]
2 years ago
5

The height of a projectile fired upward is given by the formula

Mathematics
1 answer:
natali 33 [55]2 years ago
5 0

Answer:

The projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.

Step-by-step explanation:

The height of a projectile fired upward is given by the formula:

\displaystyle s = v_{0} t - 16t^2

Where <em>s</em> is the height in feet, <em>v</em>₀ is the initial velocity, and <em>t</em> is the time in seconds.

Given a projectile with an initial velocity of 128 ft/s, we want to determine how long it will take the projectile to reach a height of 96 feet.

In other words, given that <em>v</em>₀ = 128, find <em>t</em> such that <em>s</em> = 96.

Substitute:

(96) = (128)t-16t^2

This is a quadratic. First, we can divide both sides by -16:

-6 = -8t+t^2

Isolate the equation:

t^2 - 8t + 6 = 0

The equation isn't factorable, so we can consider using the quadratic formula:

\displaystyle t = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}

In this case, <em>a</em> = 1, <em>b</em> = -8, and <em>c</em> = 6. Substitute:

\displaystyle t = \frac{-(-8)\pm\sqrt{(-8)^2-4(1)(6)}}{2(1)}

Simplify:

\displaystyle t = \frac{8\pm\sqrt{40}}{2} = \frac{8\pm 2\sqrt{10}}{2} = 4\pm \sqrt{10}

Hence, our two solutions are:

\displaystyle t = 4+\sqrt{10} \approx 7.16\text{ or } t= 4-\sqrt{10} \approx 0.84

So, the projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.

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