Question

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] ​

Answer 1

`\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,

• H is the height from which it is projected.

☯️
`\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 }}} \\`