Find t in a function when the ball hits the ground

[TempAccount]

Hello everyone, I am having some problems solving this homework problem and was wondering if anybody can step me in the right direction.

The problem basically states that a ball is falling from a building at a speed of 8 ft/s and its position is detonated by s(t) = -16t^2-8t+66, where t is time. I need to find t when the ball touches the ground.

I've tried setting s(t) to 0 and factoring (because s(t) = 0 should mark when the ball is on the ground) but I've been unable to factor this equation.

Any help would be appreciated!

 

[MarkFL]

Hello, and welcome to FMH. I've marked your question unsolved, and edited the thread title to reflect that.

Your approach is correct:

[MATH]-16t^2-8t+66=0[/MATH]
I would nxt divide through by -2:

[MATH]8t^2+4t-33=0[/MATH]
This is not going to factor with rational roots, so try applying the quadratic formula, and discard the negative root. What do you find?

 

[TempAccount]

Thank you for the reply. Upon doing the quadratic formula:

-4 +- sqr(4^2 - 4(8)(-33)) -> -4 +- sqr(16 + 1056) -> 1.7963 (rounded) and -2.29625.
---------------------------- -----------------------
2(8) 16
Discarding the negative answer reveals the right answer for t to be 1.7963. Is this correct? I tried plugging it into my online math homework but it does not accept it.

 

[TempAccount]

Nevermind, I have figured it out. 1.7963 was the correct answer, but my math homework wanted me to write it as a fraction.

For those wondering how to do this (if they stumble upon this thread later):
-4 + sqr(16 + 1056) / 16 can be split into two fractions -4 / 16 and sqr(16 + 1056)/16. The first reduces to -1/4 and the second reduces to sqr(1072)/16, this makes your final answer be -1/4 + sqr(1072)/16

 

[MarkFL]

Yes, I got:

[MATH]t=\frac{-1+\sqrt{67}}{4}\approx1.79633819296811[/MATH]
This is equivalent to what you posted, just reduced.