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

The rocket will hit the floor at 9.57 seconds

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 = (-b \± √(b^2 - 4ac))/(2a)`

Where:

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

So, we have:

`x = (-(-150) \± √((-150)^2 - 4*16*(-30)))/(2*16)`

`x = (150 \± √(22500 +1920))/(32)`

`x = (150 \± √(24420))/(32)`

`x = (150 \± 156.27)/(32)`

Split:

`x = (150 + 156.27)/(32)\ or\ (150 - 156.27)/(32)`

`x = (306.27)/(32)\ or\ (-6.27)/(32)`

Time cannot be negative;

So:

`x = (306.27)/(32)`

`x = 9.57`

Hence, the rocket will hit the floor at 9.57 seconds