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=(-b\pm √(b^2-4ac))/(2a) \\ \\=(-12\pm √(12^2-4(-16)(4)))/(2(-16)) \\ \\=(-12\pm √(144--256))/(-32) \\ \\=(-12\pm √(400))/(-32)=(-12+20)/(-32) \text{ or }(-12-20)/(-32) \\ \\=(8)/(-32) \text{ or } (-32)/(-32)=-0.25\text{ or } 1`

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