Question

If a certain cannon is fired from a height of 9.1 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 + 9.1. Find the time it takes for the cannonball to strike the ground.
The cannonball will strike the ground after about ___ seconds.
​(Type an integer or a decimal. Round to the nearest hundredth as​ needed.)  

Answer 1

Answer:

t =5.93 seconds

Step-by-step explanation:

h(t) represents the height of the cannon ball.  Zero is when the ball will hit the ground.    Substitute zero for h(t).

0 = -4.9t² + 27.5t + 9.1

This is a complicated quadratics, so we will need to use the quadratic formula to solve

-b ± sqrt(b^2 -4ac)

-----------------------------

  2a

where a = -4.9   b = 27.5   and c = 9.1

-27.5  ± sqrt(27.5 ^2 -4 (-4.9) 9.1)

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  2(-4.9)

-27.5  ± sqrt(756.25 +178.36)

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  -9.8

-27.5  ± sqrt(943.61)

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  -9.8

-27.5  ± 30.57139186

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  -9.8

3.071391856/-9.8   or  -58.07139186/-9.8

-.313407332  or  5.925652231

But time cannot be negative,  the ball cannot land before it takes off,

so t= 5.925652231 seconds

Rounding to the nearest hundredth

t =5.93 seconds

                                           

Answer 2

Answer:

The cannonball will hit the ground after about 5.926 seconds.

Step-by-step explanation:

h(t) = -4.9t² + 27.5t + 9.1

If you graphed the function on a graph, the cannonball would be hitting the ground when the function crossed the x-axis at 0. So, to solve this arithmetically, you just need to set h(t) equal to 0.

-4.9t² + 27.5t + 9.1 = 0   Plug this into a calculator if you have one, if not solve with the quadratic formula.

$\frac{-27.5 \pm \sqrt{(27.5^2) - 4(-4.9)(9.1)} }{2(-4.9)}$

t = -.0313

t = 5.9256

Since time can't be negative, you know your answer will be 5.926 seconds.