Question

An object is thrown vertically upwards and rises to a height of 80 m. Calculate the velocity with which the object was thrown upwards? G = 10m/s²
A. 40m/s

B. 50m/s

C. 80m/s

D. 10m/s

The time taken by the object to reach the highest point in the above question.
A. 4s
B. 5s
C. 8s
D. 1s
please helpp​

Answer 1

${\underline{\underline{\frak{Answer\;:}}}}$

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$\setlength{\unitlength}{1mm}\begin{picture}(8,2)\thicklines\multiput(9,1.5)(1,0){50}{\line(1,2){2}}\multiput(35,7)(0,4){13}{\line(0,1){2}}\put(10.5,6){\line(3,0){50}}\put(35,60){\circle*{10}}\put(37,7){\large\sf{u = ?}}\put(37,55){\large\sf{v = 0 m/s}}\put(18,61){\large\textsf{\textbf{Object}}}\put(30,40){\vector(0, - 4){32}}\put(30,35){\vector(0,4){22}}\put(12,35){\large\sf{s = 80 m}}\end{picture}$

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$\frak{Here} \begin{cases} & \sf{Distance\;travelled,\;s = \bf{80\;m}} \\ & \sf{Final\; velocity,\;v = \bf{0\;m/s}} \\ & \sf{g = \bf{- 10\;m/s^2}} \end{cases}$

${\underline{\sf{\bigstar\;Using\;3rd\;equation\;of\;motion\;:}}}$

$\star\;{\boxed{\sf{\purple{v^2 - u^2 = 2gs}}}}$

$:\implies\sf 0^2 - u^2 = 2 \times (- 10) \times 80$

$\: \: \qquad:\implies\sf - u^2 = - 1600$

$\qquad \: :\implies\sf \sqrt{u^2} = \sqrt{1600}$

$\qquad \: :\implies{\boxed{\frak{\pink{u = 40\;m/s}}}}\;\bigstar$

$\therefore{\underline{\sf{Initial\; Velocity\;of\;object\;is\; \bf{40\;m/s}.}}}$

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☯ Now, Finding time taken by the object to reach the highest point,

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${\underline{\sf{\bigstar\;Using\;1st;equation\;of\;motion\;:}}}$

$\star\;{\boxed{\sf{\purple{v = u + gt}}}}$

$:\implies\sf 0 = 40 + (- 10) \times t$

$:\implies\sf 0 = 40 + (- 10)\times t$

$\: \: \quad:\implies\sf 0 = 40 - 10t$

$\qquad \: \: :\implies\sf 10t = 40$

$\qquad \: \: \: :\implies\sf t = \cancel{ \dfrac{40}{10}}$

$\qquad:\implies{\boxed{\frak{\pink{t = 4\;sec}}}}\;\bigstar$

$\therefore{\underline{\sf{Time\;taken\;by\;object\;to\;reach\;the\; highest\;point\;is\; \bf{4\;sec}.}}}$

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$\qquad\qquad\;\;\;\;\qquad\boxed{\underline{\underline{\purple{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

${\underline{\sf{\bigstar\;There\;are\;three\;equation\;of\;motion\;:}}}$

$\qquad\bullet\sf\;\;\; v = u + at$

$\qquad\bullet\sf\;\;\; s = ut + \dfrac{1}{2} at^2$

$\qquad\bullet\sf\;\;\; v^2 - u^2 = 2as$

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$\quad\sf\star\;a = \dfrac{final\;velocity\;(v) - initial\;velocity\;(u)}{time\;(t)}$

$\qquad\star\;\sf g = Acceleration\;due\;to\;gravity$