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20 November, 16:10

A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. it accelerates upward at 30.0 m/s2 for 30.0s, then runs out of fuel. ignore any air resistance effects. part a what is the rocket's maximum altitude?

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  1. 20 November, 17:59
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    There are two stages to the flight: acceleration stage and deceleration stage.

    m₁ = 200 kg, mass of the rocket

    m₂ = 100 kg, mass of fuel

    a₁ = 30.0 m/s², upward acceleration when burning fuel

    Ignore air resistance and assume g = 9.8 m/s².

    Acceleration stage:

    The rocket starts from rest, therefore the initial vertical velocity is zero.

    The distance traveled is given by

    s₁ = (1/2) * (30.0 m/s²) * (30.0 s) ² = 13500 m

    Deceleration stage (due to gravity):

    The initial velocity is u = (30.0 m/s²) * (30 s) = 900 m/s

    The initial height is 13500 m

    At maximum height, the vertical velocity is zero.

    Let s₂ = the extra height traveled. Then

    (900 m/s) ² - 2 * (9.8 m/s²) * (s₂ m) = 0

    s₂ = 900²/19.6 = 41326.5 m

    The maximum altitude is

    s₁+s₂ = 54826.5 m

    Answer: 54,826.5 m
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