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Projectiles with the same speed at complementary angles (same range): heights, times or range

This type of question, asked 7 times: 2021 Paper 24, 25 Jun 2022, 25 Jan 2023, 31 Jan 2023, 29 Jan 2025, 7 Apr 2025, 8 Apr 2026 S2. All 7 questions below, oldest first.

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  1. Question 1

    2021 Paper 24

    5
    The ranges and heights for two projectiles projected with the same initial velocity at angles 42∘42^{\circ} and 48∘48^{\circ} with the horizontal are R1,R2R_{1},R_{2} and H1H_{1}, H2H_{2} respectively. Choose the correct option :

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  2. Question 2

    25 Jun 2022

    91
    Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Two identical balls A and B thrown with same velocity ' uu ' at two different angles with horizontal attained the same range RR. If AA and BB reached the maximum height h1h_{1} and h2h_{2} respectively, then R=4h1 h2R= 4\sqrt{h_{1}{\text{ }h}_{2}} Reason R: Product of said heights.
    h1 h2=(u2sin⁡2θ2 g)⋅(u2cos⁡2θ2 g)h_{1}{\text{ }h}_{2}=\left( \frac{u^{2}\sin^{2}\theta}{2\text{ }g} \right)\cdot\left( \frac{u^{2}\cos^{2}\theta}{2\text{ }g} \right)
    Choose the CORRECT answer:

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  3. Question 3

    25 Jan 2023

    104
    Two objects are projected with same velocity 'u' however 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 2 nd object will be:

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  4. Question 4

    31 Jan 2023

    112
    Two bodies are projected from ground with same speeds 40 ms−140{\text{ }ms}^{- 1} at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of 60∘60^{\circ}, with horizontal then sum of the maximum heights, attained by the two projectiles, is____ m. (Given g=10 ms−2g = 10{\text{ }ms}^{- 2} )
  5. Question 5

    29 Jan 2025

    2
    Two projectiles are fired with same initial speed from same point on ground at angles of (45∘−α)\left( 45^{\circ}- \alpha \right) and (45∘+α)\left( 45^{\circ}+ \alpha \right), respectively, with the horizontal direction. The ratio of their maximum heights attained is :

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  6. Question 6

    7 Apr 2025

    12
    Two projectiles are fired from ground with same initial speeds from same point at angles (45∘+α)\left( 45^{\circ}+\alpha \right) and (45∘−α)\left( 45^{\circ}-\alpha \right) with horizontal direction. The ratio of their times of flights is.

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  7. Question 7

    8 Apr 2026 S2

    6
    Two identical bodies projected with the same speed at two different angles cover the same horizontal range R . If the time of flight of these bodies are 5 s and 10 s , respectively, then the value of RR is ____\_\_\_\_ m. (Take g=10 m/s2g = 10\text{ }m/s^{2} )

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