A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It

Question

A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 33 ...?
A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 30 m/s^2 for 30 s, then runs out of fuel. Ignore any air resistance effects.

1) How long is the rocket in the air?
From what I already know, the 1st part of the question has been answered which is 30s, it took the rocket to get to its peak. So now I need to know the time it takes the rocket from its peak to the ground, and from the ground into the hole. So i can add all 3 times to get the ans. I'm confused on what initial and final velocities to use to solve the problem

Explanation / Answer

Velocity it attains till fuel runs out = at = 30 x 30= 900 m/s

Height it attains till fuel is present = 0.5 x a x t x t = 13500 m

Height it attains due to inertia of velocity it attained = (v x v)/2g = (900 x 900)/(2 x 9.81) = 41326.53 m

Total height it attains = 13500 m + 41326.53 m = 87050.619 m =54.826 km

Time taken for the rocket to stop = velocity it attained/g = 1155/9.81 = 91.743 s

total time spent on upward journey = 30 + 91.743 =121.74 sec

Total time the rocket was in air = 121.74 [if the rocket escapes earth]

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