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

T=5.9235 seconds

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=(-b\pm√(b^2-4ac) )/(2a)`

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

`T=(-27.52\pm√((-27.52)^2-(4*-4.9*8.9)) )/(2*-4.9)\\=(-27.52\pm√(757.3504-(-174.44)) )/(-9.8)\\=(-27.52\pm√(931.7904) )/(-9.8)\\=(-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.