More Written Homework Hints

Before I start with the hints I would like to remind you that in the original sheet I handed out there is a typo in question 2. I have fixed it in the downloads section. Also, recall that you can write up a solution to the bonus question from exam one as bonus on this assignment.  On to the hints.

1. Your best bet is to write $\mathbf{a}=\left<a_{1},a_{2},a_{3}\right>$ and grind it out. There is a clever way around this if you are interested.
2. Its hard to give a hint to this without giving it away. 
3. see earlier post.
4. Begin by building the position function for the projectile as we did in class. Once this is done you want to solve for the angle at two points.  The first of which corresponds to the rock just barely making inside the city wall, $(100,15)$. The second corresponds to the rock landing within the city while nearly going to far. I'll let you find the coordinates for this second point. During the calculation you should end up with a quadratic equation in $\tan \alpha$, where $\alpha$ is the angle. So brush up on trig identities if you get stuck.
5. This problem uses the chain rule which we only covered recently in class.  It is best to start with a two variable version of the problem and then generalize. Suppose $f(x)$ is homogeneous of degree m. Thus, 
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Now let $u=tx$ and $v=ty$ so we have

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Now take the derivative of each side of the equation with respect to $t$.  The rest follows pretty easily. I'll let you figure out the equation you want to end up with(its the 2 variable version of the one on the homework).  After working out this simplified version the version on the assignment shouldn't be so bad.

If anyone has any other hints post them in the comments.  If someone wants to post the final answer to question 4(the values of the angles) feel free, then everyone can check their work.