A fireworks rocket is launched from a hill above a lake. The rocket will fall into the lake after exploding at its maximum height. The rocket's height above the surface of the lake is given by g(x)= -16x2 + 64x + 80. How long will it take the rocket to hit the lake? A) 5 seconds B) 8 seconds C) 12 seconds D) 10 seconds

This quadratic (second degree polynomial) models parabolic motion. The vertex of the function is the projectile's max height. When the height of the object is 0 is when it hits the water. Set the function equal to 0 then and factor. I used the quadratic formula on my calculator, but if you need to, stick it into the quadratic formula and do it long hand. The values of x (which is actually time here) are -1 and 5. The two things in math that will never ever be negative are distance measurements and time, so we can disregard the -1 and say that it takes 5 seconds for the rocket to hit the water.

raphealnwobi raphealnwobi · Answer 2 · 2021-12-09T10:10:06+01:00

It would take 5 seconds for the rocket to hit the lake.

An equation is used to show the relationship between two or more variables and numbers.

Let g(x) represent the height of the rocket at time x seconds. Given that:

g(x)= -16x² + 64x + 80

The rocket touches the lake, when the height is 0. Hence:

0 = -16x² + 64x + 80

x = 5 seconds.

It would take 5 seconds for the rocket to hit the lake.

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