A stone is thrown vertically upward. When the stone is at point A, its distance from a certain point O is $$65$$ m at $$t=0$$ and the component of velocity along OA is nonzero.When it is at point $$B(OB=10$$ $$m)$$, the component of velocity along OB is zero. When it is at point C (OC=6$$ $$m), the component of velocity of the particle along OC is zero. If the velocity of projection of the stone is $$v0$$ $$=$$ $$5$$ n $$ms-1$$, then the value of n is $$_______$$.

Question

A stone is thrown vertically upward. When the stone is at point A, its distance from a certain point O is $$65$$ m at $$t=0$$ and the component of velocity along OA is nonzero.When it is at point $$B(OB=10$$ $$m)$$, the component of velocity along OB is zero. When it is at point C (OC=6$$ $$m), the component of velocity of the particle along OC is zero. If the velocity of projection of the stone is $$v0$$ $$=$$ $$5$$ n $$ms-1$$, then the value of n is $$_______$$.

Infinity Learn · Accepted Answer

From figure,$$AC=(65)2$$−$$62=65$$−$$1=12m$$ and $$CB=102$$−$$62=8m$$∴ The maximum height attained by the ball is     $$H=AB=12m+8m=20m$$∵    $$v2=u2$$−$$2gH$$ Or     $$02=v02$$−$$2gH$$∴    $$v0=2gH=2$$×$$10$$×$$20=20ms$$−$$1=5n$$∴    $$n=4$$

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