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Find the angle of projection of a projec...

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

Text Solution

Verified by Experts

The correct Answer is:
B
Given, R=H
`:. (u^2 sin2alpha)/(g) = (u^2sin^2alpha)/(2g) or 2sin alpha cos alpha = (sin^2alpha)/(2)`
or `(sinalpha)/(cosalpha) = 4 or (tanalpha)=4`
`:. alpha = tan^-1(4)`
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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^(@)`

  • 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

  • Assertion: For projection angle tan^(-1)(4) , the horizontal range and the maximum height of a projectile are equal. Reason: The maximum range of projectile is directely proportional to square of velocity and inversely proportional to acceleration due to gravity.

    A
    If both the assertion and reason are true and reason is a true explantion of the assertion.
    B
    If both the assertion and reason are true but the reason is not true the correct explantion of the assertion.
    C
    If the assertion is true but reason false
    D
    If both the assertion and reason are false.

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