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Help with max rocket height. Heights differ with methods.

  1. Sep 2, 2015 #1
    1. The problem statement, all variables and given/known data
    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 30s, then runs out of fuel. Ignore any air resistance effects. What is the rocket’s maximum altitude?

    2. Relevant equations
    Δx=V0t+(1/2)at2
    V=V0+at
    2aΔx=V2-V02

    3. The attempt at a solution
    Δx=(1/2)(30m/s2)(30s)2=13500m

    V=0(m/s)+(1/2)(30m/s2)(30s)=900m/s
    2(-9.81m/s2)Δx=02-9002m/s
    => Δx=41300m

    Total height: 55000m

    However, I did it another way and received a different result.
    V=V0+at
    0=900+(-9.81)t
    t=91.7s

    Δx=(900m/s)(91.7s)=82530m
    Total height: 96000m

    Why is this?
     
  2. jcsd
  3. Sep 2, 2015 #2

    Titan97

    User Avatar
    Gold Member

    In your second method, there is a missing ##-\frac{1}{2}gt^2## term. After it runs out of fuel, its acceleration will be g but not 0.
     
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