Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

If a certain cannon is fired from a height of 8.3 meters above the​ ground, at a certain​ angle, the height of the cannonball above the​ ground, h, in​ meters, at​ time, t, in​ seconds, is found by the function h(t) = -4.9t² + 27.5t + 8.3. Find the time it takes for the cannonball to strike the ground.

Sagot :

TheUnknownScientist

Answer:

It takes 5.89 seconds for the cannonball to strike the ground

Step-by-step explanation:

Here,

h(t) = -4.9t² + 27.5t + 8.3

To solve this arithmetically, we just need to set h(t) equal to 0.

So,

-4.9t² + 27.5t + 8.3 = 0

where,

a = -4.9; b = 27.5; c = 8.3

Now, we will use the quadratic formula.

[tex]x = \frac{-b ± \sqrt{b {}^{2} - 4ac} }{2a} \\ [/tex]

x = -27.5 ± √(27.5)² - 4(-4.9)(8.3) ÷ 2(-4.9)

x = -27.5 ± √756.25 + 162.68 ÷ (-9.8)

x = -27.5 ± √918.9 ÷ (-9.8)

x = -27.5 ± 30.3 ÷ (-9.8)

Now,

x = -27.5 + 30.3 ÷ (-9.8), x = -27.5 - 30.3 ÷ (-9.8)

x = -0.28, x = 5.89

Here, time can't be negative so x = 5.89

t = 5.89

Thus, It takes 5.89 seconds for the cannonball to strike the ground

 

-TheUnknownScientist 72

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.