Need help finishing this problem off

Can you do some algebra to separate out the factors of Vi in each term on the right-hand side?
You might want to take care in using parenthesis around (ViCos30), especially in the second term on the right-hand side.

 

Let's go slowly... do algebra first (arithmetic last). It's easier to spot an algebra mistake.

Can you factor "(ViSin30)10 * ViCos30" ?
It may help to forget the numbers and think of this symbolically as [tex](V_i A)B * V_iC[/tex]. So, can you factor this expression and write it in terms of [tex]V_i[/tex], [tex]A[/tex], [tex]B[/tex], and [tex]C[/tex]?

 

almost... correct coefficient...
check the units of that term

 

that term should have a Vi^2

 

In summary (up to this point):
ViSin(30)*10 * ViCos(30) = Vi^2 4.4

You've done fine with the coefficient, although you missed the fact that Vi is squared.
But you've gotten passed that. In other words, algebra (rather than arithmetic) is your problem.

Now, work on factoring "1/2(-9.8)(10/ViCos30)^2", which you should really write as (1/2)(-9.8)(10/ (ViCos30) )^2... especially if you try to plug something like this into your calculator.

 

I do not see anyway to give "a walk through numerically" with out doing the algebra first.

Is this the starting point:

[tex] 1.05 = V_i Sin(30) * 10 * V_i Cos(30) + \frac {-9.8} {2} \frac {10} {{(V_i Cos(30))}^2}[/tex]