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) = - 16x^2+64+80. What is the maximum height of the rocket?

A) 150 feet C) 120 feet

B) 80 feet D) 144 feet

Question

Mathematics

Rocha

10 February, 12:11

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) = - 16x^2+64+80. What is the maximum height of the rocket?

A) 150 feet C) 120 feet

B) 80 feet D) 144 feet

+2

Answers (1)

Know the Answer?

Daniella Lutz · Answer 1

D

Step-by-step explanation:

At the maximum height, the value of the vertical velocity Vy equals zero. From the value of the equation, we can get the vertical velocity by its first differential.

Differentiating this, we get - 32x + 64

We then equate this value to zero. This yield 32x = 64 and x = 2

We now plug the value of x back into the original expression for height.

-16 (2) ^2 + 64 (2) + 80 = - 64 + 128 + 80 = 144 feet