How High and Far Does a Spring-Propelled Space Shuttle Travel?

[Edgar92]

Homework Statement

The Lower Machiavellian Space Shuttle, having a total mass of 3500kg, is about to make its' debut launch. Rather then using a rocket engine to launch the shuttle, the Machiavellianans' use a large compressed spring, having a spring constant of 1600N/m. If the spring can be com[pressed by a distance of 450m and if the launching ramp is frictionless, calculate
a)the max height the space shuttle obtains, and
b)the horizontal distance the shuttle lands, as measured from the base of the ramp

*also the ramp is 45 degrees and has a height of 30m

Homework Equations

Ee=1/2kx^2
Ek=1/2mv^2
Eg=mgh

The Attempt at a Solution

Etot=Etot'
Ee=Ek+Eg
1/2kx^2=1/2mv^2+mgh
.5(1600)(450^2)=.5(3500)(v^2)+3500(9.8)(30)
162,000,000=1750v^2+1,029,000
162,000,000-1,029,000=1750v^2
160,971,000/1750=v^2
v^2=91983.4
v=303.2

from there I did sin(45)*303.2 which gave me a horz and vert speed of 214.4

vert:
1/2mv^2=mgh *im assuming 30m is ground level*
.5(214.4^2)(3500)=3500(9.8)(h)
80442880=34300h
h=80442880/34300
h=2345.27+30=2375
*that height seems very unrealistic so I'm assuming I did something wrong

 

[member 553083]

here*horz:v=d/t303.2=d/td=303.2tI'm not sure how to calculate t in this case so I'm assuming I'm wrong here too