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

t =5.93 seconds

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)

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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

The cannonball will hit the ground after about 5.926 seconds.

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.

`(-27.5 \pm √((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.