Question

Select the correct answer. A model rocket was launched from the top of a building. The rocket's approximate height can be modeled by the quadratic equation h = -4.9t2 + 53.9t + 127.4, where h is the rocket's height, in meters, after t seconds. When factored, this equation is h = -4.9(t - 13)(t + 2). What is a reasonable time for it to take the rocket to land on the ground? Answer A 11 seconds Answer B 13 seconds Answer C 2 seconds Answer D 15 seconds

Answer 1

13 seconds.

Explanation:

Given

`h = -4.9(t - 13)(t + 2).`

Required

Determine a reasonable solution for t

To do this, we equate h to 0.

`h = -4.9(t - 13)(t + 2).` becomes

`0 = -4.9(t - 13)(t + 2).`

Divide through by -4.9

`0 = (t - 13)(t + 2).`

Reorder the expression

`(t - 13)(t + 2) = 0.`

Split

`t-13 = 0` or
`t + 2 = 0`

This gives:

`t = 13` or
`t = -2`

But time can't be negative, So:

`t = 13`