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Maximum height reached when projected with a fraction (1/2 or 1/3) of escape velocity

The same question, asked 4 times: 10 May 2024 S2, 12 May 2024 S2*, 20 Apr 2025 S1*, 13 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    10 May 2024 S2

    43
    A body is projected vertically from earth's surface with velocity equal to half the escape velocity. The maximum height reached by the satellite is (R=R= radius of earth)

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  2. Question 2

    12 May 2024 S2

    44
    A body is projected vertically upwards from earth's surface of radius 'RR' with velocity equal to 13\frac{1}{3}rd of escape velocity. The maximum height reached by the body

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  3. Question 3

    20 Apr 2025 S1

    33
    A body is projected vertically from earth's surface with (13)rd \left( \frac{1}{3} \right)^{\text{rd~}} of escape velocity. The maximum height reached by the body is ( R=R = radius of earth)

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  4. Question 4

    13 Apr 2026 S1

    109
    A body is projected vertically from earth's surface of radius R with velocity equal to half the escape velocity. The maximum height reached by the body is

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