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Find the angle of projection for a proje...

Find the angle of projection for a projectile motion whose rang `R` is (n) time the maximum height `H`.

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To solve the problem of finding the angle of projection for a projectile motion where the range \( R \) is \( n \) times the maximum height \( H \), we can follow these steps: ### Step 1: Write the formulas for Range and Maximum Height The formulas for the range \( R \) and maximum height \( H \) of a projectile are given by: - Range: \[ R = \frac{u^2 \sin 2\theta}{g} \] ...
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Find the angle of projection of a porjectile for which for horizontal range and maximum height are equal.

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Knowledge Check

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

    A
    `alpha = tan^-1(2)`
    B
    `alpha = tan^-1(4)`
    C
    `alpha = tan^-1(5)`
    D
    None of the above
  • 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
  • If R is the range of a projectiel on a horizontal plane and h its maximum height, the maximum horizontal range with the same velocity of projection is:

    A
    2h
    B
    `(R^(2))/(8h)`
    C
    `2R+(h^(2))/(8R)`
    D
    `2h+(R^(2))/(8h)`
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    For which angle of projection the horizontal range is 5 times the maximum height attrained ?

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

    A cannon fires its projectile with such an initial velocity and angle of projection that its range is R and the maximum height to which the projectile rises is H. Find the maximum range that can be obtained with the same initial velocity.

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    Show that the horizontal range of a projectile is same for two angles of projection . Is the sum of maximum heights for these two angles dependent on the angle of projectile ?