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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

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