Answer:
930.7 m
Explanation:
After starting from rest with a constant acceleration of 29.4m/s2 for 3.98 s it would have achieved a speed of
[tex]v = a\Delta t = 29.4*3.98 = 117.012 m/s[/tex]
And a height of
[tex]h_1 = at^2/2 = 232.85 m[/tex]
After 3.98s it runs out of fuel, so gravity is the only force exerted on the rocket. As it reaches its maximum height, its kinetic energy is converted to potential energy:
[tex]E_p = E_k[/tex]
[tex]mgh_2 = mv^2/2[/tex]
where m is the mass and [tex]h_2[/tex] is the vertical distance traveled from the point where it runs out of fuel to the maximum height, v is the velocity at the point here it runs out of fuel. g = 9.81m/s2 is the gravitational acceleration
[tex]9.81h_2 = 117.012^2/2[/tex]
[tex]h_2 = \frac{117.012^2}{2*9.81} = 697.85 m [/tex]
So the total distance it has traveled from ground is
[tex]h = h_1 + h_2 = 697.85 + 232.85 = 930.7 m[/tex]
