Question

PLEASE HELP ASAP!!!!!!!!
The function below represents the height, in feet, of the rocket, and t represents the time, in seconds, since the rocket was launched.

h(t) = -16t^2 + 72t + 7

State how long it takes the rocket to hit the ground to the nearest tenth of a second as only a number without units.

Answer 1

Answer:

4.6.

Step-by-step explanation:

The rocket hits the ground when h(t) = 0. So

$-16t^{2} + 72t + 7 = 0$

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$.

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$, given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$-16t^{2} + 72t + 7 = 0$

So

$a = -16, b = 72, c = 7$

Then

$\bigtriangleup = 72^{2} - 4*(-16)*7 = 5632$

$t_{1} = \frac{-72 + \sqrt{5632}}{2*(-16)} = -0.1$

$t_{2} = \frac{-72 - \sqrt{5632}}{2*(-16)} = 4.6$

Time is a positive measure, so the answer is 4.6.