A NCC parade is going at a uniform speed of 9,km / h under a mango tree on which a monkey is sitting

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3-2.Motion in Plane

medium

A $NCC$ parade is going at a uniform speed of $9\,km / h$ under a mango tree on which a monkey is sitting at a height of $19.6\,m$. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is $...m$
(Given $g=9.8\,m / s ^{2}$ )

A$5$

B$10$

C$19.8$

D$24.5$

(JEE MAIN-2022)

Solution

Time taken by mango $=\sqrt{\frac{2 h}{g}}$
$=\sqrt{\frac{2 \times 19.6}{9.8}}=2 \text { second }$
Distance $= vt$
$=9 \times \frac{5}{18} \times 2=5\,m$

Standard 11

Physics

The position of a particle is given by

$r=3.0 t \hat{i}+2.0 t^{2} \hat{j}+5.0 \hat{k}$

where $t$ is in seconds and the coefficients have the proper units for $r$ to be in metres.

$(a)$ Find $v (t)$ and $a (t)$ of the particle.

$(b)$ Find the magnitude and direction of $v (t)$ at $t=1.0 s$

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hard

A $NCC$ parade is going at a uniform speed of $9\,km / h$ under a mango tree on which a monkey is sitting at a height of $19.6\,m$. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is $...m$ (Given $g=9.8\,m / s ^{2}$ )

Solution

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A $NCC$ parade is going at a uniform speed of $9\,km / h$ under a mango tree on which a monkey is sitting at a height of $19.6\,m$. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is $...m$
(Given $g=9.8\,m / s ^{2}$ )

The position of a particle is given by

$r=3.0 t \hat{i}+2.0 t^{2} \hat{j}+5.0 \hat{k}$

where $t$ is in seconds and the coefficients have the proper units for $r$ to be in metres.

$(a)$ Find $v (t)$ and $a (t)$ of the particle.

$(b)$ Find the magnitude and direction of $v (t)$ at $t=1.0 s$