Question

If a certain canon is fired from a height of 8.9 m above the ground, at a certain angle, the height of the Campbell above the ground, age, and meters, at times, tea, and second, is found by the function of age parentheses T equals -4.9 T squared +27.52+8.9. Find the time it takes for the cannonball to strike the ground

Answer 1

Answer:

T=5.9235 seconds

Step-by-step explanation:

$H(T)= -4.9T^2+27.52T+8.9.$

The time it takes for the cannonball to strike the ground is the point at which H(T)=0

$H(T)= -4.9T^2+27.52T+8.9.=0$

$-4.9T^2+27.52T+8.9=0$

This is a quadratic equation and since we have a bunch of decimals we use the quadratic formula:

$x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}$

a=-4,9, b=27.52, c=8.9

$T=\dfrac{-27.52\pm\sqrt{(-27.52)^2-(4*-4.9*8.9)} }{2*-4.9}\\=\dfrac{-27.52\pm\sqrt{757.3504-(-174.44)} }{-9.8}\\=\dfrac{-27.52\pm\sqrt{931.7904} }{-9.8}\\=\dfrac{-27.52\pm30.53 }{-9.8}\\T=-0.3071 \:or\: 5.9235\\T=5.9235 seconds$

It takes 5.9235 seconds for the cannonball to strike the ground.