5. A rocket engine can accelerate a rocket launched from rest vertically up with a constant acceleration of 20.00 m/s$^2$. However, at an altitude of 12250 m the engine fails. (a) How much time did the rocket engine work? (b) What is the velocity of the rocket at the moment the engine failed? (c) What maximum height above the Earth does the rocket reach? Take $g = 9.81 ext{ m/s}^2$ and show all your work.
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Given: Initial velocity (u) = 0 m/s, acceleration (a) = 20 m/s², final altitude (s) = 12250 m Using the kinematic equation: s = ut + (1/2)at² 12250 = 0 + (1/2)(20)t² 24500 = 10t² t² = 2450 t = √2450 t ≈ 49.5 seconds Therefore, the rocket engine worked for 49.5 Show more…
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