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For which angle of projection the horizo...

For which angle of projection the horizontal range is 5 times the maximum height attrained ?

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To solve the problem of finding the angle of projection for which the horizontal range is 5 times the maximum height attained, we can follow these steps: ### Step 1: Understand the formulas The horizontal range \( R \) and maximum height \( H \) for a projectile launched with an initial velocity \( u \) at an angle \( \theta \) are given by the following formulas: - Horizontal Range: \[ R = \frac{u^2 \sin 2\theta}{g} \] ...
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Find the angle of projection at which horizontal range and maximum height are equal.

Find the angle of projection for which the horizontal range and the maximum height are equal.

Knowledge Check

  • Assertion: In projectile motion, when horizontal range is n times the maximum height, the angle of projection is given by tan theta=(4)/(n) Reason: In the case of horizontal projection the vertical increases with time.

    A
    If both assertion `&` Reason are True `&` the Reason is a corrrect explanation of the Asserion.
    B
    If both Assertion `&` Reason are True but Reason is not correct explanation of the Assertion.
    C
    If Assertion is Trie but the Reason is False.
    D
    If both Assertion `&` Reason are false
  • For an object projected from ground with speed u horizontal range is two times the maximum height attained by it. The horizontal range of object is

    A
    `(2u^(2))/(3g)`
    B
    `(3u^(2))/(4g)`
    C
    `(3u^(2))/(2g)`
    D
    `(4u^(2))/(5g)`
  • For given value of u, there are two angles of projection for which the horizontal range is the same. the sum of the maximum heights for these two angles is

    A
    independent of the angle of projection
    B
    dependent of the angle of projection.
    C
    May depend on angle of projection
    D
    None of the above
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