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Standard XII

Physics

Direction of Instantaneous Velocity

A small spher...

Question

A small sphere is projected with a velocity of $3$ m s $^{- 1}$ in a direction $60^{o}$ from the horizontal y-axis, on the smooth inclined plane . The motion of sphere takes place in the x-y plane. Calculate the magnitude $v$ of its velocity after $2 s$ .

3.5 m s^{- 1}

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1.5 m s^{- 1}

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2.5 m s^{- 1}

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4.5 m s^{- 1}

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Solution

The correct option is B $1.5 m s^{- 1}$
The motion of the sphere takes place in a plane ; the $x -$ and $y -$ components of its acceleration are $A_{x} = - g sin 30^{o}, a_{y} = 0$ .The $x -$ and $y -$ components of the sphere's velocity at time t= $2 s$ are
$V_{x} = v_{0 x} - a_{x} t = 3 sin 60^{o} - g sin 30^{o} \times 2 = 0.1 m s^{- 1}$
$V_{y} = v {cos}^{60^{o}} = c o n s t a n t = 1.5 m s^{- 1}$
so the magnitude of sphere's velocity is
$| ¯ v | = \sqrt{v_{x}^{2} + v_{y}^{2}} = \sqrt{(0.1)^{2} + (1.5)^{2}} = 1.5 m s^{- 1}$

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A small sphere is projected with a velocity of 3 m s−1 in a direction 60o from the horizontal y-axis, on the smooth inclined plane . The motion of sphere takes place in the x-y plane. Calculate the magnitude v of its velocity after 2s.

A small sphere is projected with a velocity of $3$ m s $^{- 1}$ in a direction $60^{o}$ from the horizontal y-axis, on the smooth inclined plane . The motion of sphere takes place in the x-y plane. Calculate the magnitude $v$ of its velocity after $2 s$ .