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Maximum height or range of two projectiles thrown at different angles

This type of question, asked 4 times: 16 Apr 2026 S2, 17 Apr 2026 S1, 20 Apr 2026 S2, 13 May 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    16 Apr 2026 S2

    103
    Two objects are projected with same velocity 'u' at different angles α\alpha and β\beta with the horizontal. If α+β=90∘\alpha + \beta = 90^\circ, the ratio of horizontal range of the first object to the second object will be [sin⁡(π−θ)=sin⁡θ][\sin(\pi - \theta) = \sin\theta]

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  2. Question 2

    17 Apr 2026 S1

    103
    Two balls A and B are projected at an angle of 45∘45^\circ and 60∘60^\circ respectively, so that the maximum heights reached are same for both. The ratio of initial velocity of projection of ball A to that for ball B is (sin⁡30∘=cos⁡60∘=12, sin⁡45∘=cos⁡45∘=12, sin⁡60∘=cos⁡30∘=32)\left(\sin 30^\circ = \cos 60^\circ = \dfrac{1}{2},\ \sin 45^\circ = \cos 45^\circ = \dfrac{1}{\sqrt{2}},\ \sin 60^\circ = \cos 30^\circ = \dfrac{\sqrt{3}}{2}\right)

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  3. Question 3

    20 Apr 2026 S2

    105
    Two spheres are projected at angles 30∘30^\circ and 45∘45^\circ with the horizontal. The maximum height reached by both is same. The ratio of their initial velocities is, (sin⁡45∘=12,sin⁡30∘=0.5)\left(\sin 45^\circ = \dfrac{1}{\sqrt{2}}, \sin 30^\circ = 0.5\right)

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  4. Question 4

    13 May 2026 S2

    103
    If two spheres are projected at angles 45∘45^\circ and 60∘60^\circ with horizontal and the maximum heights reached are same. The ratio of their initial velocities is (sin⁡45∘=12,sin⁡60∘=32)\left(\sin 45^\circ = \dfrac{1}{\sqrt{2}}, \sin 60^\circ = \dfrac{\sqrt{3}}{2}\right)

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