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Ratio of potential energies at the highest point: thrown vertically vs at an angle with the same speed

The same question, asked 2 times: 3 May 2023 S1*, 9 May 2024 S1. Every wording below, oldest first.

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  1. Question 1

    3 May 2023 S1

    1
    A ball 'A' is projected vertically upwards with certain initial speed. Another ball 'B' of same mass is projected at an angle of 30∘30^\circ with vertical with the same initial speed. At the highest point, the ratio of potential energy of ball A to that of ball B will be [sin⁡90∘=1, sin⁡60∘=cos⁡30∘=32, sin⁡30∘=cos⁡60∘=12\sin 90^\circ=1,\ \sin 60^\circ=\cos 30^\circ=\frac{\sqrt{3}}{2},\ \sin 30^\circ=\cos 60^\circ=\frac{1}{2}]

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  2. Question 2

    9 May 2024 S1

    42
    A stone is projected vertically upwards with speed 'VV'. Another stone of same mass is projected at an angle of 60∘60^\circ with the vertical with the same speed 'VV'. The ratio of their potential energies at the highest points of their journey is

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