Question

A rocket takes off from a height of 30 feet with an initial velocity of 150 ft /sec. The equation that models the path that the rocket takes is: G(x) = -16x^2+150x+30

Answer 1

Answer:

The rocket will hit the floor at 9.57 seconds

Step-by-step explanation:

Given

$G(x) = -16x^2 + 150x + 30$

Take off height = 30ft

Initial velocity= 150ft/s

Required [Missing from the question]

Time to hit the ground

The rocket will hit the ground at:

$G(x) = 0$

So, we have:

$0 = -16x^2 + 150x + 30$

Rewrite as:

$16x^2 - 150x - 30=0$

Solve using quadratic formula, we have:

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

Where:

$a= 16\\ b = -150\\ c = -30$

So, we have:

$x = \frac{-(-150) \± \sqrt{(-150)^2 - 4*16*(-30)}}{2*16}$

$x = \frac{150 \± \sqrt{22500 +1920}}{32}$

$x = \frac{150 \± \sqrt{24420}}{32}$

$x = \frac{150 \± 156.27}{32}$

Split:

$x = \frac{150 + 156.27}{32}\ or\ \frac{150 - 156.27}{32}$

$x = \frac{306.27}{32}\ or\ \frac{-6.27}{32}$

Time cannot be negative;

So:

$x = \frac{306.27}{32}$

$x = 9.57$

Hence, the rocket will hit the floor at 9.57 seconds