Question

7. A ball is gently dropped from a height of 20 m. If its velocity
increases uniformly at the rate of 10 m s2, with what velocity
will it strike the ground? After what time will it strike the
ground?
To
19​

Answer 1

${\underline{\underline{\sf{\red{{\bigstar}\:\:\:Given:-}}}}}$

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$\begin{gathered}\:\:\:\:\bullet\:\:\:\sf\orange{Height \ (s) = 20m }\\\:\:\:\:\bullet\:\:\:\sf\green{Acceleration \ (a) = 10m/s^2}\end{gathered}$

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${\underline{\underline{\sf{\orange{{\bigstar}\:\:\:To~Find:-}}}}}$

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$\begin{gathered}\:\:\:\:\bullet\:\:\:\sf\purple{What\: velocity\: will\: it\: strike\: the\: ground}\\\:\:\:\:\bullet\:\:\:\sf\red{What \ time \ will \ it \ strike \ the \ ground}\end{gathered}$

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${\underline{\underline{\sf{\blue{{\bigstar}\:\:\: Solution:-}}}}}$

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$\dag\:\underline{\mathfrak{\purple{Using\: 3rd\: equation \:of \:motion }}}$

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$\red{\underline{\boxed{\sf{v^2 = u^2 + 2as}}}}$

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${\underline{\sf{\:\:\:\:Where,\:\:\:}}}$

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$\begin{gathered}\:\:\:\:\bullet\:\:\:\sf\orange{v = final \:velocity}\\ \:\:\:\:\bullet\:\:\:\sf\green{u = initial \:velocity}\\ \:\:\:\:\bullet\:\:\:\sf\blue{a = acceleration\: or \:deceleration}\\\:\:\:\:\bullet\:\:\:\sf\red{s = displacement}\end{gathered}$

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$\dag\:\underline{\mathfrak{\purple{Substituting \: the \: values}}}$

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$\qquad\quad\rightarrow\:\:\:\:\sf{ v^2 = 0+2\times 10\times 20}$

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$\qquad\quad\rightarrow\:\:\:\:\sf{ v^2 = 400}$

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$\qquad\quad\rightarrow\:\:\:\:\sf{v = 20m/s}$

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$\dag\:\underline{\mathfrak{\purple{Using\: 1st\: equation \:of \:motion }}}$

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$\red{\underline{\boxed{\sf{v = u + at}}}}$

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${\underline{\sf{\:\:\:\:Where,\:\:\:}}}$

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$\begin{gathered}\:\:\:\:\bullet\:\:\:\sf\orange{v = final \:velocity}\\ \:\:\:\:\bullet\:\:\:\sf\green{u = initial \:velocity}\\ \:\:\:\:\bullet\:\:\:\sf\blue{a = acceleration\: or \:deceleration}\\ \:\:\:\:\bullet\:\:\:\sf\red{t = time}\end{gathered}$

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$\dag\:\underline{\mathfrak{\purple{Substituting \: the \: values}}}$

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$\qquad\quad\rightarrow\:\:\:\:\sf{t = \frac{v-u}{a}}$

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$\qquad\quad\rightarrow\:\:\:\:\sf{t = \frac{20}{10}}$

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$\qquad\quad\rightarrow\:\:\:\:\sf{t = 2s}$