A particle is projected vertically upwards with a speed of $$16$$ $$ms-1$$. After some time, when it again passes through the point of projection, its speed is found to be $$8$$ $$ms-1$$. It is known that the work done by air resistance is same during upward and downward motion. Then the maximum height attained by the particle is (take$$ g $$=$$ $$10$$ $$ms-2)

Question

A particle is projected vertically upwards with a speed of $$16$$ $$ms-1$$. After some time, when it again passes through the point of projection, its speed is found to be $$8$$ $$ms-1$$. It is known that the work done by air resistance is same during upward and downward motion. Then the maximum height attained by the particle is (take$$ g $$=$$ $$10$$ $$ms-2)

Infinity Learn · Accepted Answer

From $$work-energy$$ theorem, for upward motion $$12m(16)2=$$ $$mgh$$ $$+$$ W (work$$ done by air $$resistance) for downward motion,$$12m(8)2$$  $$=$$ $$mgh$$ – W ⇒  [$$(16)2$$ $$+(8)2$$] $$=$$ $$2ghor$$  h $$=$$ $$8$$ m

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