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Question

A body is projected vertically up with u. Its velocity at half its maximum height is?


A
u2
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B
u22
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C
2u
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D
u2
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Solution

The correct option is D $$\displaystyle\frac{u}{\sqrt{2}}$$
For a body projected up,
$${ H }_{ max }=\cfrac { { u }^{ 2 } }{ 2g } $$
By equation
$${ v }^{ 2 }={ u }^{ 2 }-2gh$$
Putting, $$h=\cfrac { { H }_{ max } }{ 2 } =\cfrac { { u }^{ 2 } }{ 4g } $$
$${ v }^{ 2 }={ u }^{ 2 }-2g{ v }^{ 2 }={ u }^{ 2 }-2g\cfrac { { u }^{ 2 } }{ 4g } $$
$$={ u }^{ 2 }-\cfrac { { u }^{ 2 } }{ 2 } $$
$${ v }^{ 2 }=\cfrac { { u }^{ 2 } }{ 2 } $$
$$v=\cfrac { u }{ \sqrt { 2 }  } $$

Physics

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