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

Answer:

5.16 seconds

Step-by-step 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:

$t-2=$±$\sqrt{10}$

$t=2$±$\sqrt{10}$

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

$t=2+\sqrt{10}$

$t=2+3.16$

$t=5.16$