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A ball rolls from the edge of the top step of a stair case with horizontal speed `5ms^(-1)` .Each step is of 2m high and 1m width.The ball hits nth step then 'n' is `(g=10m/s^(2))`

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A ball rolls off top of a staircase with a horizontal velocity u m s^-1 . If the steps are h metre high and b mere wide, the ball will just hit the edge of n th step. Find the value of n .

Velocity at a general point P(x, y) for a horizontal projectile motion is given by v=sqrt((v_("x")^(2)+v_("y")"^(2))),tan alpha=(v_(y))/(v_(x)) alpha is angle made by v with horizontal in clockwise direction Trajectory equation for a horizontal projectile motion is given by x=v_(x)t=ut y=- (1//2)"gt"^(2) eliminating t, we get y=-(1//2)(gx^(2))/(u^(2) A ball rolls off top of a stair way with a horizontal velocity u m//s. If the steps are h m high and b meters wide, the ball will just hit the edge of nth step if n^(th) equals to

Knowledge Check

  • A ball rolls off the top of a staircase with a horizontal velocity u m//s . If the steps are h meter high and b meter wide, the ball will hit the edge of the nth steps, if:

    A
    `n=(2hu)/(gb^(2))`
    B
    `n=(2hu^(2))/(gb)`
    C
    `n=(2hu^(2))/(gb^(2))`
    D
    `n=(hu^(2))/(gb^(2))`
  • A ball rolls of the top fi a strair way with horizonntal velocity of magnitude 1. 8 ms^(-1) . The steps are 0.20 m high and 0.02 m wide , Which step will the ball it first ? ( g = 10 m//s^@) .

    A
    (a) both Assertion and Reason are true and the Reason is correct explanation of the Assertion .
    B
    (b )both Assertion and Reason are true but the Reason is not a correct explanation of the Assertion.
    C
    (C ) Assertion is true but the Reason is false.
    D
    (d) both Assertion and Reason are false.
  • A ball rolls of the top of a stair way with a horizontal velocity u m s^(-1) . If the steps are h metre high and b metre wide, the time taken by the ball to hit the edge of n^(th) step, is

    A
    `(hu)/(gb)`
    B
    `(2hu)/(gb)`
    C
    `(2hu^2)/(gb)`
    D
    `(hu^2)/(2gb)`
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