Extra credit problems dealing with projectiles

[Lightening Lover]

"extra credit" problems dealing with projectiles

My physics prof. gave us the following "extra credit" problems dealing with projectiles, but there are two different ones, and therefor there will be two different color, lol but yeah here you go:
The first problem reads as following:
You are in the amry and unfortunately you are at a disadvangtage, for your enemy is on top of a hill 100 meters high, the center of the hill is 500 meters away. You have one projectiles which on it, the tag reads that it shoots at an initial velocity of 5meters/second. You have to find the angle at which you must fire the projectile, so that it travels up above the enemy's hill and comes straight dowm to hit the enemy.
Now there are 2 solutions to this problem, and I know that you need the higher one of the two, but I have no clue on how to solve it.
The second problem reads as following: You are rolling a ball down a set of stairs, your initial velocity is v m/s, the hieght of the stairs (or the riser) is y, the treads (or bases of the stairs) are x. The object of this problem is to find a formula that will have the variables v, y,x,(as defined earlier), n(the number of steps) and a (gravitational pull aka 9.81). You must have it in the fashion ofn=the equation. However the only catch is that the equation must deliver whole numbers.
For this one I know how to get the whole numbers however, I don't know the equation.
Any help at all on either problems would be greatly appreciated

 

[cow_gone_mad]

Well the first problem is pretty simple. Since it is in 2 dimensions and you know the starting speed v0 = (5cos(a), 5sin(a)) where a is the angle you fire the projectile off, and you know the acceleration a = (0, -g).

For second problem, what kind of formula are you looking for?