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Llana [10]
3 years ago
10

If a certain cannon is fired from a height of 8.8 meters above the​ ground, at a certain​ angle, the height of the cannonball ab

ove the​ ground, h, in​ meters, at​ time, t, in​ seconds, is found by the function h left parenthesis t right parenthesis equals negative 4.9 t squared plus 30.5 t plus 8.8. Find the time it takes for the cannonball to strike the ground.
Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
6 0

Answer:

It would take approximately 6.50 second for the cannonball to strike the ground.

Step-by-step explanation:

Consider the provided function.

h(t)=-4.9t^2+30.5t+8.8

We need to find the time takes for the cannonball to strike the ground.

Substitute h(t) = 0 in above function.

-4.9t^2+30.5t+8.8=0

Multiply both sides by 10.

-49t^2+305t+88=0

For a quadratic equation of the form ax^2+bx+c=0 the solutions are: x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

Substitute a = -49, b = 305 and c=88

t=\frac{-305+\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}=-\frac{-305+\sqrt{110273}}{98}\\t = \frac{-305-\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}= \frac{305+\sqrt{110273}}{98}

Ignore the negative value of t as time can't be a negative number.

Thus,

t=\frac{305+\sqrt{110273}}{98}\approx6.50

Hence, it would take approximately 6.50 second for the cannonball to strike the ground.

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