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A body projected with the same velocity ...

A body projected with the same velocity at two different angles covers the same horizontal distance R.If t and t' are the two times of flight, prove that `R=1/2 gtt'`

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A body projected with the same velocity at two different angles covers the same horizontal distance R. If t and t' are two times of flight, prove that R=1/2 gtt .

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Knowledge Check

  • 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 are projected upwards with the same initial velocity v_(0) in two different angles of projection such that their horizontal ranges are the same. The ratio of the heights of their horizontal ranges are the same. The ratio of the heights of their highest point will be

    A
    `tan^(2) theta_(1)`
    B
    `v_(0)^(2) sin^(2) theta_(1)`
    C
    `v_(0) sin theta_(1)`
    D
    `v_(0)//cos theta_(1)`

  • Two particles are projected from the same point with the same speed at different angles theta_(1) and theta_(2) to the horizontal. If their respective times of flights are T_(1) and T_(2) and horizontal ranges are same then a) theta_(1)+theta_(2)=90^(@) , b) T_(1) =T_(2)tan theta_(1) c. T_(1) =T_(2)tan theta_(2) , d) T_(1)sin theta_(2)=T_(2)sin theta_(1)

    A
    `a,b,d`are correct
    B
    `a,c,d`are correct
    C
    `b,c,d`are correct
    D
    `a,b,c`are correct

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