Answer
Verified
397.5k+ views
Hint: Use kinematics equation to calculate the velocity at the starting of last $2s$.From this value of velocity calculate the distance covered in the first half by the kinematics formula. Total height of the tower will be the sum of both the heights.
Formula used:
$s=ut+\dfrac{1}{2}a{{t}^{2}}$
Where, $s=\text{displacement, }u=\text{ initial velocity,}a=\text{ acceleration}$
If particle falls under influence of gravity then $a=g=\text{ acceleration due to gravity}$
${{v}^{2}}-{{u}^{2}}=2as$
Where ,
$\begin{align}
& v=\text{ final velocity of the particle} \\
& u\text{ =initial velocity of particle} \\
& s\text{ =displacement} \\
& a\text{=acceleration} \\
\end{align}$
Complete step by step answer:
Suppose the height of the tower is $H$. When the particle is at height $h=H-40$, let its velocity be . So when the particle is at height $'h'$ from the top let its velocity be $'u'$. According to the question the particle covers the last $40m$ in $2\sec $.
$s=ut+\dfrac{1}{2}g{{t}^{2}}$
Here $s=40m$,$t=2\sec $,$g=\text{ acceleration due to gravity=}10m{{s}^{-2}}$
Putting these values we get.
$\begin{align}
& 40=u\times 2+\dfrac{1}{2}\times 10\times {{2}^{2}} \\
& \Rightarrow 40=2u+20 \\
& \Rightarrow 2u=20 \\
& \Rightarrow u=10m{{s}^{-1}} \\
\end{align}$
i.e. when the particle starts to cover the last $40m$ distance its velocity is $10m{{s}^{-1}}$.
When the object dropped from the top of the tower its initial velocity is $u'=0$. After covering the distance $'h'$ its final velocity will be the initial velocity of the object when it starts to cover the last $40m$ which is $v=10m{{s}^{-1}}$.
According to formula ${{v}^{2}}-{{u}^{2}}=2as$
Here $v=10m{{s}^{-1}},u=u'=0,a=g=10m{{s}^{-2}}\text{ and }s=h$
Now
$\begin{align}
& {{10}^{2}}-{{0}^{2}}=2\times 10\times h \\
& \Rightarrow 20h=100 \\
& \Rightarrow h=5m \\
\end{align}$
Total height of tower is $H+h=40m+5m=45m$
Additional Information
If a particle has initial velocity $u$ have constant acceleration $a$in time $t$ then the final velocity is given by $v=u+at$
Note:
All the equation of kinematics $v=u+at$,${{v}^{2}}-{{u}^{2}}=2as$,and $s=ut+\dfrac{1}{2}g{{t}^{2}}$ can be used only for uniformly accelerated motion. It is not valid for the motion where the acceleration changes with time. Also if a particle falls under the influence of gravity(free fall) the acceleration of the object is constant and is equal to acceleration due to gravity. If an object is thrown upward then $a=-g$ and of falls then $a=g$.
Formula used:
$s=ut+\dfrac{1}{2}a{{t}^{2}}$
Where, $s=\text{displacement, }u=\text{ initial velocity,}a=\text{ acceleration}$
If particle falls under influence of gravity then $a=g=\text{ acceleration due to gravity}$
${{v}^{2}}-{{u}^{2}}=2as$
Where ,
$\begin{align}
& v=\text{ final velocity of the particle} \\
& u\text{ =initial velocity of particle} \\
& s\text{ =displacement} \\
& a\text{=acceleration} \\
\end{align}$
Complete step by step answer:
Suppose the height of the tower is $H$. When the particle is at height $h=H-40$, let its velocity be . So when the particle is at height $'h'$ from the top let its velocity be $'u'$. According to the question the particle covers the last $40m$ in $2\sec $.
$s=ut+\dfrac{1}{2}g{{t}^{2}}$
Here $s=40m$,$t=2\sec $,$g=\text{ acceleration due to gravity=}10m{{s}^{-2}}$
Putting these values we get.
$\begin{align}
& 40=u\times 2+\dfrac{1}{2}\times 10\times {{2}^{2}} \\
& \Rightarrow 40=2u+20 \\
& \Rightarrow 2u=20 \\
& \Rightarrow u=10m{{s}^{-1}} \\
\end{align}$
i.e. when the particle starts to cover the last $40m$ distance its velocity is $10m{{s}^{-1}}$.
When the object dropped from the top of the tower its initial velocity is $u'=0$. After covering the distance $'h'$ its final velocity will be the initial velocity of the object when it starts to cover the last $40m$ which is $v=10m{{s}^{-1}}$.
According to formula ${{v}^{2}}-{{u}^{2}}=2as$
Here $v=10m{{s}^{-1}},u=u'=0,a=g=10m{{s}^{-2}}\text{ and }s=h$
Now
$\begin{align}
& {{10}^{2}}-{{0}^{2}}=2\times 10\times h \\
& \Rightarrow 20h=100 \\
& \Rightarrow h=5m \\
\end{align}$
Total height of tower is $H+h=40m+5m=45m$
Additional Information
If a particle has initial velocity $u$ have constant acceleration $a$in time $t$ then the final velocity is given by $v=u+at$
Note:
All the equation of kinematics $v=u+at$,${{v}^{2}}-{{u}^{2}}=2as$,and $s=ut+\dfrac{1}{2}g{{t}^{2}}$ can be used only for uniformly accelerated motion. It is not valid for the motion where the acceleration changes with time. Also if a particle falls under the influence of gravity(free fall) the acceleration of the object is constant and is equal to acceleration due to gravity. If an object is thrown upward then $a=-g$ and of falls then $a=g$.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Write an application to the principal requesting five class 10 english CBSE
Difference Between Plant Cell and Animal Cell
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Discuss what these phrases mean to you A a yellow wood class 9 english CBSE
List some examples of Rabi and Kharif crops class 8 biology CBSE