Projectile motion in kinematics

[Lightening Lover]

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 50meters/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

 

[Mathechyst]

Only 5 meters per second?

Doug

 

[nautica]

You will have 2 answers for the first problem - one will be on the way up and one on the way down - if the projectile will reach, then you will use the later of the two - if not, your army is screwed.

Nautica

 

[Lightening Lover]

fixing mistakes

for the first reply, no I'm sorry it is 50m/s not 5m/s, sry about that, I changed it now though.
And for the second reply, that is not correct, because the shape that the projectile would take is a parabola, and if you look below at the diagrames you can see that there are two possible ways to hit the hill(btw sry about the diagram, can't do anything on my computer right)

***** __**********************imagine that the lines are curves
*****/**\********************and you are at x, and the enemy at e
****/****\******************and the stars are spaces
***/*****e********OR**********_'e
**/*****/*\******************_'*/*\
*/*****/**\****************_'**/***\
x'****/****\************x'****/*****\
this diagram shows/////while this one shows
how the projectile/////that the projectile
would first go up//////would hit the enemy
and then com down//////from the side
to hit the enemy///////(or before the
(or after the////////// turning point)
turning point)