After a vertical launch, the rocket moved for 30 seconds with an acceleration of 30 m / s ^ 2.

After a vertical launch, the rocket moved for 30 seconds with an acceleration of 30 m / s ^ 2. After 30 seconds, the engines were turned off. How high was the rocket able to climb?

Given: t1 (time of accelerated movement) = 30 s; a1 (first acceleration) = 30 m / s2; t1 (slow motion time) = 30 s; a2 (second acceleration) = g ≈ 10 m / s2.

To find the height of the rocket rise, we use the formula: H = S1 + S2 = a1 * t1 ^ 2/2 + V1 * t2 – a2 * t2 ^ 2/2 = a1 * t1 ^ 2/2 + V1 * V1 / g – g * (V1 / g) ^ 2/2 = a1 * t1 ^ 2/2 + V1 ^ 2 / g – V1 ^ 2 / 2g = a1 * t1 ^ 2/2 + V12 / 2g = a1 * t1 ^ 2/2 + (a1 * t1) ^ 2 / 2g.

Calculation: H = 30 * 30 ^ 2/2 + (30 * 30) ^ 2 / (2 * 10) = 13500 + 40500 = 54,000 m (54 km).