initial displacement = dboost = v0t + 1/2at^2
hboost = dboost sin theta
xboost = dboost cos theta
vboost = v0 + at
vxboost = vboost cos theta
vyboost = vboost sin theta
To get the maximum altitude, use conservation of energy
initial PE + vertical KE
= mg (hboost) + 1/2 m vyboost^2
= final PE = mg (hfinal)
hfinal = hboost + vyboost^2 / 2g
= hboost + ((v0 + at) * sin (theta))^2 / 2g
b) flight time =
boost time + time to rise ballistically from hboost to hfinal
+ time to fall from hfinal
The time to fall a distance h can be gotten by:
h = 1/2 gt^2, so t = sqrt (h/2g)
So flight time = t + sqrt ((hfinal - hboost)/2g)+ sqrt (hfinal/2g)
Horizontal range = xboost + vxboost * time of ballistic flight
= (v0t + 1/2at^2) cos theta
+ (v0 + at) cos theta * (sqrt ((hfinal - hboost)/2g)+ sqrt (hfinal/2g))
Lots of plugging and chugging to do now.
EDIT--the problem said acceleration was constant, so we don't have to worry about loss of mass during the boost. Realistic? No. But that's what the problem says. Once the thing is ballistic, it's a moot point anyway
