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Question

Two bodies are projected vertically upwards from one point with the same initial velocity $$\displaystyle v_{0}.$$ The second body is projected $$\displaystyle t_{0}s$$ after the first. How long after will the bodies meet?


A
v02g+t02
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B
v0g+t02
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C
v0g+t04
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D
2v0g+t02
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Solution

The correct option is B $$\displaystyle \dfrac{v_{0}}{g}+\dfrac{t_{0}}{2}$$

$$the\quad displacement\quad of\quad the\quad two\quad bodies\quad should\quad be\quad same\quad when\quad they\quad collide\\ h\quad =\quad { v }_{ 0 }t-\dfrac { 1 }{ 2 } g{ t }^{ 2 }={ v }_{ 0 }(t-{ t }_{ 0 })-\dfrac { 1 }{ 2 } g{ (t-{ t }_{ 0 }) }^{ 2 }\Rightarrow t=\dfrac { { v }_{ 0 } }{ g } +\dfrac { { t }_{ 0 } }{ 2 } $$


Physics

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