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$0 - 730 m = v_0 * \sin(-37)(5s) - \frac{1}{2}(9.8)(5s)$

How is this equation solved? The book says the answer is $v_0 = 202$, but when I ran the calculations it was $-33$.

Here's the page from the book:

enter image description here I did $\sin(-37)$, times $5$. Then did the $1/2$ stuff. Then subtracted the $\sin$ equation, then $-730/$stuff and got $-33$.

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I got 202 just fine, you forgot to square time in the second term. Always start with the equation first, don't just plug in numbers or you'll miss something like that.

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    I was about to fix the equation, as I thought this was a typo! – 2017-02-14