I came across the following physics exercise:
A high-powered 7-mm Remington magnum rifle fires a bullet with a velocity of $900$ m/s on a rifle range. Neglect air resistance.
(a) Calculate the distance $h$ such a bullet will drop at a range of $200$ m when fired horizontally.
(b) To compensate for the drop of the bullet, when the telescope sight is pointed right at the target, the barrel of the gun is aligned to be slanted slightly upward, pointed a distance $h$ above the target. The downward fall due to gravity then makes the bullet strike the target as desired. Suppose, however, such a rifle is fired uphill at a target $200$ m distance. If the upward slope of the hill is $45^\circ$, should you aim above or below the target, and by how much? What should you do when shooting on a downhill slope at $45^\circ$ below horizontal?
Part (a) was easy as $\pi$. However, regarding part (b), I'm in trouble. Intuitively, I'd imagine to aim a bit higher uphill and downhill, just like on a horizontal plane. But, according to the book, I'm wrong: I need to aim lower! Why!?