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A rocket is launched vertically from Earth's surface with a velocity of 3.4 km/s. How high does it go:
From Earth's centre?
From Earth's surface?

how can this be done without any time or force mentioned ??

  • physics -

    vₒ= 3.4 km/s= 3400 m/s.
    The problem may be solved by several methods.
    The first method (kinematics)
    The height from the Earth's surface
    h =vₒ•t -g•t²/2,
    At the top point v=0, => vₒ=g•t, t = vₒ/g,
    Substitute it in the equation for h and obtain
    h=vₒ²/2•g =(3400 )²/2•9.8 ≈ 5.9•10^5 m. =590 km.
    The second method (the law of conservation of energy)
    KE = ΔPE.
    m•v²/2 = m•g•h,
    h = vₒ²/2•g =….
    The Earth’s radius is R ≈ 6378 km.
    The distance from Earth's centre is
    H = 6378 + 590 = 6968 km.

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