Question

a ball is thrown vertically upwards with a velocity of 56m/s calculate (a) the maximum height to which it rises (b) the total time it takes to riturn to the surface of the earth​

Answer 1

AnsweR :-

• Initial Velocity (u) = 56 m/s

• Final Velocity (v) = 0 m/s

• Acceleration due to gravity = -10 m/s²

We are asked to find the maximum height to which it rises and the total time it takes to return to the surface of the earth.

$\begin{gathered}\bigstar \: \underline{\textbf{ Maximum height to which it rises : } } \\ \end{gathered}$ 

Using third kinematical equation of motion we can find the maximum height to which ball rises :

$\begin{gathered}:\implies\sf v^2 - u^2 = 2gh \\ \\ \end{gathered}$ 

$\begin{gathered}:\implies\sf h = \dfrac{v^2- u^2}{2g} \\ \\ \end{gathered}$ 

$\begin{gathered}:\implies\sf h = \dfrac{(0)^2- (56)^2}{2 \times ( - 10)} \\ \\ \end{gathered}$ 

$\begin{gathered}:\implies\sf h = \dfrac{- (56)^2}{ - 20} \\ \\ \end{gathered}$ 

$\begin{gathered}:\implies\sf h = \dfrac{(56)^2}{ 20} \\ \\ \end{gathered}$ 

$\begin{gathered}:\implies\sf h = \dfrac{3136}{ 20} \\ \\ \end{gathered}$ 

$\begin{gathered}:\implies \underline{ \boxed{\frak{ h = 156.8 \: m}}} \\ \\ \end{gathered}$ 

$\begin{gathered}\therefore\:\underline{\textsf{The maximum height to which it rises is \textbf{156.8 m}}}. \\ \end{gathered}$ 

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$\begin{gathered}\bigstar \: \underline{\textbf{ Time taken : } } \\ \end{gathered}$ 

$\begin{gathered}\dashrightarrow\:\:\sf v = u + gt \\ \\ \end{gathered}$ 

$\begin{gathered}\dashrightarrow\:\:\sf v - u = gt \\ \\ \end{gathered}$ 

$\begin{gathered}\dashrightarrow\:\:\sf \dfrac{v - u }{g}= t \\ \\ \end{gathered}$ 

$\begin{gathered}\dashrightarrow\:\:\sf t = \dfrac{v - u }{g}\\ \\ \end{gathered}$ 

$\begin{gathered}\dashrightarrow\:\:\sf t = \dfrac{0 - 56}{ - 10}\\ \\\end{gathered}$ 

$\begin{gathered}\dashrightarrow\:\:\sf t = \dfrac{ - 56 }{ - 10}\\ \\\end{gathered}$ 

$\begin{gathered}\dashrightarrow\:\:\sf t = \dfrac{56 }{10}\\ \\\end{gathered}$ 

$\begin{gathered}\dashrightarrow\:\: \underline{ \boxed{\frak{ t = 5.6 \: s}}}\\ \\\end{gathered}$ 

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$\begin{gathered}\bigstar \: \underline{\textbf{ The total time it takes to return to the surface of the earth : } } \\ \end{gathered}$ 

 

$\begin{gathered}\longrightarrow\:\:\textsf {Total time = Time of ascesnd + Time of descend} \\ \\ \end{gathered}$

$\begin{gathered}\longrightarrow\:\:\textsf {Total time = 5.6 + 5.6} \\ \\ \end{gathered}$

$\begin{gathered}\longrightarrow\:\: \underline{ \boxed{\frak {Total \: time = 11.2 \: s}}} \\ \\ \end{gathered}$ 

$\begin{gathered}\therefore\:\underline{\textsf{The total time it takes to return to the surface of the earth is \textbf{ 11.2 second}}}. \\ \end{gathered}$

Answer 2

Answer:

height= 156.8m

time = 11.2seconds

Explanation:

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