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Speed or energy of a projectile at its highest point or at a later point

This type of question, asked 4 times: 19 Apr 2025 S2, 15 Apr 2026 S2, 17 Apr 2026 S2, 13 May 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    19 Apr 2025 S2

    20
    A stone is projected with kinetic energy E, making an angle θ\theta with the horizontal. When it reaches a highest point, its kinetic energy is

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  2. Question 2

    15 Apr 2026 S2

    103
    A batsman hits a ball with a velocity 'v', making an angle of 60∘60^\circ with the vertical. After some time direction of velocity is making an angle of 60∘60^\circ with the horizontal. The speed of the ball at this instant is [cos⁡(60∘)=12,cos⁡(30∘)=32]\left[\cos(60^\circ) = \dfrac{1}{2}, \cos(30^\circ) = \dfrac{\sqrt{3}}{2}\right]

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  3. Question 3

    17 Apr 2026 S2

    103
    A ball P is projected at an angle of 60∘60^\circ with the vertical with certain initial speed. Another ball Q of the same mass as that of ball P is projected vertically upwards with the same initial speed as that of P. At the highest point, the ratio of potential energy of ball P to that of ball Q is (sin⁡30∘=0.5)(\sin 30^\circ = 0.5)

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  4. Question 4

    13 May 2026 S1

    103
    A particle is projected from ground with speed u and at an angle θ\theta with horizontal. If at maximum height from ground, the speed of a particle is half times its initial velocity of projection then its maximum height attained is (cos⁡60∘=0.5,sin⁡60∘=3/2)(\cos 60^\circ = 0.5, \sin 60^\circ = \sqrt{3}/2) (g = acceleration due to gravity)

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