A rocket, initially at rest on the ground, accelerates straight upward with a co

Question

A rocket, initially at rest on the ground, accelerates straight upward with a constant acceleration of 58.8 m/s2 . The rocket accelerates for a period of 9.00s before exhausting its fuel. The rocket continues its ascent until its motion is halted by gravity. The rocket then enters free fall.

Find the maximum height, , reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity of 9.810 m/s2 ?
I have the first part when the fuel is exausted the hieght is 2380m but I can't figure out the second part.
A rocket, initially at rest on the ground, accelerates straight upward with a constant acceleration of 58.8 m/s2 . The rocket accelerates for a period of 9.00s before exhausting its fuel. The rocket continues its ascent until its motion is halted by gravity. The rocket then enters free fall.

Find the maximum height, , reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity of 9.810 m/s2 ?
I have the first part when the fuel is exausted the hieght is 2380m but I can't figure out the second part.

Explanation / Answer

initial velocity u = 0 acceleration a = 58.8m/s2 final velocity v = u + at = 0 + 58.8*9 = 529.2m/s v2 - u2 = 2ah1 529.2^2 = 2*58.8*h1 => h1 = 2380m for second part initial velocity u = 529.2m/s acceleration a = -9.81m/s2 final velocity = 0m/s v2-u2 = 2ah2 =>0-529.2^2 = 2*-9.81*h2 =>h2 = 14274m so, total height = h1+h2 = 14274 + 2380 = 16654m

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