Acceleration/Velocity/Position Problem

[lorrelle1]

My homework assignment is on integral word problems, and I am very stuck on this problem! It reads as follows:
With what initial velocity must an object be thrown upward (from ground level) to reach the top of the Washington Monument (approximately 550 feet)?
And this is what I have done:
let n=time at the maximum height
s(n)=550
v(n)=0 or s'(n)=0
a(n)=-32ft/sec or s''(n)=-32
s(0)=0

indefinite integral(-32)dx
-32n+c=v(n) (let c be any constant)
indefinite integral(-32n+c)dx
-16nsquared+cn+b=s(n) (let b be another constant)
plug in the s(0)=0 and you get b=0, so
s(n)=-16nsquared+cn
.....and now what? i have a position equation but i cannot plug in the s(n)=550 because of the c. i might be missing something obvious, or on the wrong path entirely, but I can't seem to figure out how to finish this problem! Please help me...

 

[Deleted member 4993]

My homework assignment is on integral word problems, and I am very stuck on this problem! It reads as follows:
With what initial velocity must an object be thrown upward (from ground level) to reach the top of the Washington Monument (approximately 550 feet)?
And this is what I have done:
let n=time at the maximum height
s(n)=550
v(n)=0 or s'(n)=0
a(n)=-32ft/sec or s''(n)=-32
s(0)=0

indefinite integral(-32)dt
-32t+c=v(t) (let c be any constant)

at t= n, v(t) = 0

c = 32n

v(t) = 32(n-t)


indefinite integral

\(\displaystyle s(t) \, = \, \int [32(n-t)] dt\)

now continue...
-16nsquared+cn+b=s(n) (let b be another constant)
plug in the s(0)=0 and you get b=0, so
s(n)=-16nsquared+cn
.....and now what? i have a position equation but i cannot plug in the s(n)=550 because of the c. i might be missing something obvious, or on the wrong path entirely, but I can't seem to figure out how to finish this problem! Please help me...