Answer:
44.64 seconds
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration due to gravity = 9.8 m/s²
[tex]v^2-u^2=2as\\\Rightarrow v=\sqrt{2as+u^2}\\\Rightarrow v=\sqrt{2\times 4.2\times 1180+80.6^2}\\\Rightarrow v=128.01\ m/s[/tex]
[tex]v=u+at\\\Rightarrow 128.01=80.6+4.2t\\\Rightarrow t=\frac{128.01-80.6}{4.2}=11.29\ s[/tex]
Time taken to reach 1180 m is 11.29 seconds
[tex]v=u+at\\\Rightarrow 0=128.01-9.8t\\\Rightarrow t=\frac{128.01}{9.8}=13.06\ s[/tex]
Time the rocket will keep going up after the engines shut off is 13.06 seconds.
[tex]v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{0^2-128.01^2}{2\times -9.8}\\\Rightarrow s=836.05\ m[/tex]
The distance the rocket will keep going up after the engines shut off is 836.05 m
Total distance traveled by the rocket in the upward direction is 1180+836.05 = 2016.05 m
The rocket will fall from this height
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow 2016.05=0t+\frac{1}{2}\times 9.8\times t^2\\\Rightarrow t=\sqrt{\frac{2016.05\times 2}{9.8}}\\\Rightarrow t=20.29\ s[/tex]
Time taken by the rocket to fall from maximum height is 20.29 seconds
Time the rocket will stay in the air is 11.29+13.06+20.29 = 44.64 seconds