Conceptual problem with projectile motion

[1MileCrash]

Homework Statement

[PLAIN]http://img23.imageshack.us/img23/4554/physicshomework.png

Homework Equations

The Attempt at a Solution

I have the right answer because it is obvious, but I wanted to practice working this out regardless, and I have something slightly different for hmax.

First, I found the y-component of velocity to be:

V_{o}sin\theta_{o} - 9.8t

It follows that at the highest point, that this is equal to 0. So I set it equal to 0 and solved for t.

t = \frac{V_{o}sin\theta_{o}}{9.8}

Integrating my y velocity gives y position:

y(t) = (V_{o}sin\theta_{o})t - 4.9t^{2}

And solving for our time gives me:

h_{max} = V_{o}sin\theta_{o}(\frac{V_{o}sin\theta_{o}}{9.8}) - 4.9(\frac{V_{o}sin\theta_{o}}{9.8})^{2}

Where did I go wrong?

Thanks!

EDIT nevermind! They are the same, just had to do some algebra.

 

[Dick]

The first thing you did wrong is writing 9.8 instead of g. If you go back and fix that and do a little algebra you'll see you already have the same answer as in the image.

 

[1MileCrash]

I'm not sure why you think that's wrong, I didn't forget halfway through the problem that they are the same..

 

[Dick]

I'm not sure why you think that's wrong, I didn't forget halfway through the problem that they are the same..

It's wrong because now you have to change 9.8 back to g and 4.9 back to g/2. Why didn't you just leave it g to begin with? That's what I mean by 'wrong'. It's sort of a tactical error. You're making life complicated by leaving numbers floating around instead of 'g'.

 

[1MileCrash]

Not sure, I just wrote it that way without thinking. What I meant was that I didn't get to the end and say "they have g where I have 9.8, what is going on."