Question

A ball is dropped from a building at the same time a balloon rises from the ground. The heights, in feet, of the ball and balloon above the ground after x seconds are modeled by the functions below. Ball: f(x)=24−16x2Balloon: g(x)=4x After how many seconds are the ball and the balloon at the same height? Use a graphing calculator and round to the nearest hundredth. A. 1.36 B. 4.42 C. 1.11 D. 5.42

Answer 1

C. 1.11

Explanation:

Ball: f(x) = 24 − 16x^2

Balloon: g(x) = 4x

4x = 24 - 16x^2

16x^2 + 4x - 24 = 0

4x^2 + x - 6 = 0

`x = (-b \pm √(b^2 - 4ac))/(2a)`

`x = (-1 \pm √(1^2 - 4(4)(-6)))/(2(4))`

`x = (-1 \pm √(1 + 96))/(8)`

`x = (-1 \pm √(97))/(8)`

`x = (-1 + √(97))/(8)` or
`x = (-1 - √(97))/(8)`

We discard the negative solution.

`x = 1.11`

Answer: C. 1.11