Answer:
Y=1370.23m
Explanation:
The motion have two moments the first one the time the initial velocity is accelerating then when the engines proceeds to move as a projectile
[tex]a=19 \frac{m}{s^{2} } \\voy=vo*sin(\alpha )\\voy=90*sin(39 )\\y_{o}=0m\\y_{f}=y_{o}+v_{oy}*t+\frac{1}{2}*a*t^{2}\\y_{f}=90*sin(39)*7s+\frac{1}{2}*19\frac{m}{s^{2} }*(7)^{2}\\y_{f}=861.97m[/tex]
Now the motion the rocket moves as a projectile so:
[tex]v_{fy}=v_{iy}+a*t\\v_{fy}=90+9.8*7\\v_{fy}=158.6 sin(39)[/tex]
Now the final velocity is the initial in the second one
[tex]v_{fy}^{2}=v_{fi}^{2}+2*a*yf \\\\a=g\\[/tex]
The maximum altitude Vf=0
[tex]0=v_{fi}^{2}+2*a*yf \\\\yf=\frac{(158.6 sin(39))^{2} }{2*9.8\frac{m}{s^{2} } } \\yf=508.26m[/tex]
So total altitude is both altitude of the motion so:
[tex]Y=508.2m+861.97m\\Y=1370.23m[/tex]
