A stone is projected horizontally from the top of a cliff with a velocity of 12 ms¯¹. If it reached the ground 2s later, calculate the height of the cliff. [g = 10 m/s]

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asked Jun 1, 2024 174k views

1 Answer

Max Macfarlane · Answer 1 · 2024-06-07T05:23:33+0000

$\red{\frak{Given}}\begin{cases}\textsf{Horizontal velocity of projection is 12m/s.}\\\textsf{ It reaches ground 2s later.} \\\end{cases}$

To find :- Height of the cliff .

$\qquad\qquad\rule{100}1$

If a particle is projected Horizontally, from a certain height, then time of flight is given as ,

$\longrightarrow\sf \red{ Time_(of \ flight) =\sqrt{(2H)/(g)} }\\$

where,

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$\underline{\underline{\boldsymbol{ According \ to \ the \ question \ :- }}}$

$\longrightarrow\sf \sqrt{(2H)/(g)} = 2s \\$

$\longrightarrow\sf\left( \sqrt{(2H)/(g)} \right)^2 =( 2s )^2 \\$

$\longrightarrow\sf (2H)/(10\ m/s^2)= 4s^2 \\$

$\longrightarrow\sf H = (4 * 10)/(2) m \\$

$\longrightarrow\sf \underline{\underline{\red{ Height_(of \ cliff )= 20m }}} \\$