Answer:
8271.92 m
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration
Equation of motion
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow s=0\times t+\frac{1}{2}\times 18\times 18^2\\\Rightarrow s=2916\ m[/tex]
The height reached at 18 seconds is 2916 m
[tex]v=u+at\\\Rightarrow v=0+18\times 18\\\Rightarrow v=324\ m/s[/tex]
The velocity at 2916 m is 324 m/s
[tex]v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{0^2-324^2}{2\times -9.8}\\\Rightarrow s=5355.92\ m[/tex]
Maximum height reached by the toy rocket is 2916+5355.92 = 8271.92 m
The maximum height above the ground that the rocket will achieve is 8,271.92m.
To get the maximum height, we need to calculate the height reached by the rocket.
Using the equation:
[tex]S=ut+\frac{1}{2}at^2\\S =0(t) + \frac{1}{2}\times18\times 18^2\\S=9 \times 18^2\\S=2,916m[/tex]
Get the velocity also using the equation of motion:
[tex]v=u+at\\v=0+18(18)\\v=324m/s[/tex]
Get the maximum height above the ground the rocket will achieve:
[tex]v^2=u^2+2as\\324^2=0^2+2(9.8)s\\104,976=19.6s\\s=\frac{104,976}{19.6}\\s= 5,355.92m[/tex]
The total maximum height reached by rocket is 2,916 + 5,355.92 = 8,271.92m.
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