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Two particles projected form the same po...

Two particles projected form the same point with same speed u at angles of projection `alpha and beta` strike the horizontal ground at the same point. If `h_1 and h_2` are the maximum heights attained by the projectile, R is the range for both and `t_1 and t_2` are their times of flights, respectively, then

A

`alpha + beta = pi/2`

B

`R = 4(sqrt(h_1h_2))`

C

`t_1/t_2 = tan alpha`

D

`tan alpha = (sqrt (h_1/h_2))`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`alpha + beta = 90^@` or `beta = 90^@ - alpha`
`h_1= (u^2sin^2alpha)/(2g) and h_2 = (u^2cos^2alpha)/(2g)`
`t_1 = (2usinalpha)/g and t_2 = (2ucosalpha)/g`
`R_1 = R_2 = (2u^2sinalphacosalpha)/g = R` .
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Knowledge Check

  • The horizontal range is four times the maximum height attained by a projectile. The angle of projection is

    A
    `90^(@)`
    B
    `60^(@)`
    C
    `45^(@)`
    D
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  • Two particles are projected from the same point with the same speed at different angles theta_1 & theta_2 to the horizontal. They have the same range. Their times of flight are t_1 & t_2 respectily

    A
    `(t_1)/(t_2)=tan^2theta_1`
    B
    `(t_1)/(sintheta_1)=(t_2)/(costheta_2)`
    C
    `(t_1)/(t_2)=tantheta_1`
    D
    `(t_1)/(t_2)=tan^2theta_2`

  • Two particles A and B are projected from the same point with the same speed but at different angles alpha and beta with the horizontal, such that the maximum height of A is two-third of the horizontal range of B .Then which of the following realtions are true ?

    A
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    B
    `3(1-cos 2 alpha)=8 sin 2 beta`
    C
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    D
    maximum horizontal range of `A` =`u^(2)//g` and this occurs when `beta=1/2sin^(-1)(3/8)`

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