Question

Hope is performing her juggling act using several balls. She throws the balls up at an initial height of 4 feet, with a speed of 12 feet per second. If Hope doesn't catch one of the balls, about how long does it take the ball to hit the floor?

Hint: Use H(t) = −16t2 + vt + s.


A. 6.25 seconds

B. 1.15 seconds

C. 1.00 second

D. 0.22 second

Answer 1

The correct answer is C) 1.00 seconds.

Using the initial velocity and initial height given, the equation is:

H(t) = -16t²+12t + 4

We set this equal to 0 to solve it:
0 = -16t²+12t+4

We will use the quadratic formula to solve this:
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\=\frac{-12\pm \sqrt{12^2-4(-16)(4)}}{2(-16)} \\ \\=\frac{-12\pm \sqrt{144--256}}{-32} \\ \\=\frac{-12\pm \sqrt{400}}{-32}=\frac{-12+20}{-32} \text{ or }\frac{-12-20}{-32} \\ \\=\frac{8}{-32} \text{ or } \frac{-32}{-32}=-0.25\text{ or } 1$

Since a negative number makes no sense for time, it must be that t=1 second.