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A cannon fires its projectile with such ...

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.

Text Solution

Verified by Experts

The correct Answer is:
`R_("max")=2H+R^2/(8H)`
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An object is projected so that its horizontal range R is maximum. If the maximum height of projectile is H , find the value of H//R .

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Knowledge Check

  • The angle of projection at which the horizontal range and maximum height of projectile are equal is

    A
    `45^@`
    B
    `theta = tan^(-1) (0.25)`
    C
    `theta = tan^(-1) (4)`
    D
    `60^(@)`

  • An object is projected with speed u and range of the projectile is found to be double of the maximum height attained by it . Range of the projectile is .

    A
    `(2u^(2))/(5g)`
    B
    `(3u^(2))/(5g)`
    C
    `(4u^(2))/(5g)`
    D
    `(u^(2))/(g)`

  • An object is projected with speed u and range of the projectile is found to be double of the maximum height attained by it . Range of the projectile is .

    A
    `v_(A)=v_(B)=v_(C)`
    B
    `v_(A) gt v_(B) gt v_(C)`
    C
    `v_(A) lt v_(B) lt v_(C)`
    D
    `v_(a)=v_(B) gt v_(C)`

    • Similar Questions

    Explore conceptually related problems

    A projectile is thrown with an initial velocity of v = a hat i + b hat j . If the range of projectile is double the maximum height reached by it. Find the ratio (b)/(a) .

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

    The maximum range of a projecitle fired with some initial velocity is found to be 1000 metre The maximum height (H) reached by this projectile is:-

    The range of a projectile for a given initial velocity is maximum when the angle of projection is 45^(@) . The range will be minimum, if the angle of projection is

    A projectile has a range of 40 m and reaches a maximum height of 10 m . Find the angle at which the projectile is fired.

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