PWN the SAT Math Guide p. 122 (p. 120 in newer printing) #9

h = -4.9^2 + t + 1.5
The equation … After how many seconds will the coin land on the ground?

When the coin lands, y=0, so we just need to solve the quadratic. Using the quadratic formula, however, I get a messy repeating decimal, not .664, .665. Could you solve this for me using the quadratic formula?

Also, I tried to search the Q&A here to see if you had already answered this question. Could you make an index for PWN the SAT Math Gu

Sure. In the book, I solve this by graphing—which, as you know from reading my book, I love to do. 🙂 But of course we should also land on the same result using the quadratic formula.

    \begin{align*}0=-4.9t^2+t+1.5\end{align*}

    \begin{align*}t&=\dfrac{-1\pm\sqrt{1^2-4(-4.9)(1.5)}}{2(-4.9)}\\\\t&=\dfrac{-1\pm\sqrt{30.4}}{-9.8}\\\\t&=\dfrac{-1}{-9.8}\pm\dfrac{\sqrt{30.4}}{-9.8}\end{align*}

At this point you’re going to have to enter everything into your calculator (in fact, you probably did that a few steps ago!) to see where everything lands. You’ll get a negative number (t = –0.46…) that you can ignore, and the positive number you want: = 0.664655…

As for an index for PWN questions, I don’t get all that many so I haven’t bothered with an index. Between the solutions at the end of the book and the videos in the Owners Area (for the chapters that have them) I guess people are mostly OK! Of course, I’m quite happy to post solutions here, too, so you should feel free to submit without checking. If, on the off chance, I’ve posted a solution before, I’ll link to it.