The rocket is launched vertically upward. The rocket engines give it an acceleration of 40 m / s2.

The rocket is launched vertically upward. The rocket engines give it an acceleration of 40 m / s2. How long does it take for the rocket to hit the ground if the fuel burns out after 2 minutes?

a = 40 m / s ^ 2.

t1 = 2 min = 120 s.

g = 9.8 m / s ^ 2.

t -?

The rocket flight time t will be the sum of the ascent time tpod and the lowering time top: t = tpod + top.

Let’s find the speed V1, and the height of the rocket ascent h1 before the engine is turned off.

V1 = a * t1, h1 = a * t1 ^ 2/2.

V1 = 40 m / s ^ 2 * 120 s = 4800 m / s.

h1 = 40 m / s ^ 2 * (120 s) ^ 2/2 = 288000 m.

After turning off the engines, the rocket will first move up to a complete stop, and then down.

The rocket travel time from turning off the engines to stopping is t2 = V1 / g.

t2 = 4800 m / s / 9.8 m / s ^ 2 = 490 s.

The height from turning off the engine to a complete stop of the ship is found by the formula: h2 = g * t2 ^ 2/2.

h2 = 9.8 m / s ^ 2 * (490 s) ^ 2/2 = 1175530 m.

The time and height of the rocket rise will be determined by the formulas: tp = t1 + t2, hp = h1 + h2.

hsub = 288000 m + 1175530 m = 1463530 m.

tp = 120 s + 490 s = 610 s.

Let us find the free fall time of the rocket top from the height hs.

top = √ (2 * hp / g).

top = √ (2 * 1463530 m / 9.8 m / s ^ 2) = 546.5 s.

t = 610 s + 546.5 = 1156.5 s.

Answer: the rocket flight time is t = 1156.5 s.