Answer:
3091.56
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration due to gravity = 9.81 m/s² (positive downward and negative upward)
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow s=0\times 25+\frac{1}{2}\times 3.5\times 25^2\\\Rightarrow s=1093.75\ m[/tex]
Distance traveled in the first stage is 1093.75 m
[tex]v=u+at\\\Rightarrow v=0+3.5\times 25\\\Rightarrow v=87.5\ m/s[/tex]
Velocity at the end of first stage is 87.5 m/s
[tex]v=u+at\\\Rightarrow a=\frac{v-u}{t}\\\Rightarrow a=\frac{132.5-87.5}{10}\\\Rightarrow a=4.5\ m/s^2[/tex]
Acceleration of the second stage is 4.5 m/s²
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow s=87.5\times 10+\frac{1}{2}\times 4.5\times 10^2\\\Rightarrow s=1100\ m[/tex]
Distance traveled in the second stage is 1100 m
[tex]v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{0^2-132.5^2}{2\times -9.81}\\\Rightarrow s=894.81\ m[/tex]
Distance traveled after the second stage has stopped firing is 894.81 m
Total height the rocket reached = 1093.75+1100+897.81 = 3091.56 m
