The case will automatically open if you get a higher score than Kate's on the archery board. So let's get shooting!
Hint 2
Click on the straw bales to start a round. The bow comes with a red target circle to show you where you're shooting, which is nice; but the targets move, which isn't.
Hint 3
The circles on the targets give you a higher score as you move in to the center. The orange dot at the center is 20 points; the yellow circle is 15 points; the red circle is 10 points; the blue circle is 5 points; the grey circle is 2 points; and hitting the white part or the straw bales is 0 points.
Hint 4
Amateurs need to beat a score of 37, which isn't horribly hard; Masters need to get more than 55, which is daunting but also not impossible.
Hint 5
The trick here, if it is a trick, is to shoot where the target is going to be when the arrow reaches it. If you had to map this out, it would require the more elevated forms of calculus; in the non-mathematical world, it's a matter of hand-eye coordination and intuition. And guessing, of course.
Hint 6
The best way I've found to hit the point I'm after is to draw the arrow and hold it, then go to a spot exactly level with the bullseye but to the right of the target. Release the arrow when the target is still a beat away from being where the red target circle is.
Hint 7
Exactly how far away it should be and when to release is a matter of practice, I'm afraid. But there's no penalty for missing, and shooting arrows is actually kind of fun. (Especially in a computer game where you don't have to gather the arrows that missed.)