Question

Little Frufru is standing at the top of a lighthouse. She is 96 feet above the ocean. She tosses a ball into the air. The height, h, of the ball after x

seconds is given by h = - 16t2 +64t +96. How many seconds does it take the ball to land in the ocean? Round to the neaest hundredth

Answer 1

5.16 seconds

Explanation:

Think about a graph with h(t) as the y-axis, and t as the x-axis. Meaning at the start (0 seconds) the ball will be at 96 feet in the air (hence the constant/y-int). We want to see when that ball hits the exactly 0 feet. Which means it needs to touch the x-axis. So h(t) must equal 0. We can subtitute this in the equation:

`h(t)=- 16t^2 +64t +96`

`0=- 16t^2 +64t +96`

Now we just need to find the factors. First we should make the coefficient 0 by adding everything to the left side:

`16t^2 -64t -96=0`

Now divide both sides by 16:

`t^2 -4t -6=0`

Now we can Use the complete the square method:

`t^2-4t=6`

Take have of 4 and then square it and add it to both sides:

`t^2-4t+4=10`

`(t-2)^2=10`

Square both sides:

`t-2=`±
`√(10)`

`t=2`±
`√(10)`

Then, since it is only positive time you would get:

`t=2+√(10)`

`t=2+3.16`

`t=5.16`