Answer
435.3k+ views
Hint: When a body is dropped from some height then initial velocity of the body is zero and the acceleration of the body is equal to the acceleration due to gravity. The motion of the body during free fall is uniform accelerated motion. As the motion of the body is uniformly accelerated, hence the equation of motion can be applied to calculate the unknown terms.
Complete step by step solution:
Height of the skyscraper, $H=320m$
According to equations of the motion, the student having a free fall can be described by the following equation.
$s=ut+\dfrac{1}{2}a{{t}^{2}}$
Where,
$s=$Displacement
$u=$Initial velocity$=0m/s$
$a=$Acceleration$=10m/{{s}^{2}}$
$t=$Time taken by the body
Then,
Putting the values in the equation of motion,
$\begin{align}
& 320=\left( 0 \right)t+\dfrac{1}{2}\left( 10 \right){{t}^{2}} \\
& {{t}^{2}}=64 \\
& t=8s \\
\end{align}$
So, the total time taken by the student for the free fall from the skyscraper is 8s.
It is given that Superman arrives after 5 s, so the time taken by Superman to reach the bottom of the skyscraper to save the student is
$\left( 8-5 \right)s=3s$
Superman has taken 3s to cover the total height of the skyscraper.
Again, using the equation of motion $s=ut+\dfrac{1}{2}a{{t}^{2}}$
Assuming $u$as the initial velocity of Superman
$\begin{align}
& 320=3u+\dfrac{1}{2}\left( 10 \right){{\left( 3 \right)}^{2}} \\
& 3u=320-45 \\
& u=\dfrac{275}{3}m/s \\
& =91.67m/s
\end{align}$
Therefore, to save the student the superman must have velocity equal or greater than 91.67 m/s.
Note: - It is assumed that the acceleration due to gravity is uniform on the surface of the earth.
- It is assumed that the air resistance is negligible.
Complete step by step solution:
Height of the skyscraper, $H=320m$
According to equations of the motion, the student having a free fall can be described by the following equation.
$s=ut+\dfrac{1}{2}a{{t}^{2}}$
Where,
$s=$Displacement
$u=$Initial velocity$=0m/s$
$a=$Acceleration$=10m/{{s}^{2}}$
$t=$Time taken by the body
Then,
Putting the values in the equation of motion,
$\begin{align}
& 320=\left( 0 \right)t+\dfrac{1}{2}\left( 10 \right){{t}^{2}} \\
& {{t}^{2}}=64 \\
& t=8s \\
\end{align}$
So, the total time taken by the student for the free fall from the skyscraper is 8s.
It is given that Superman arrives after 5 s, so the time taken by Superman to reach the bottom of the skyscraper to save the student is
$\left( 8-5 \right)s=3s$
Superman has taken 3s to cover the total height of the skyscraper.
Again, using the equation of motion $s=ut+\dfrac{1}{2}a{{t}^{2}}$
Assuming $u$as the initial velocity of Superman
$\begin{align}
& 320=3u+\dfrac{1}{2}\left( 10 \right){{\left( 3 \right)}^{2}} \\
& 3u=320-45 \\
& u=\dfrac{275}{3}m/s \\
& =91.67m/s
\end{align}$
Therefore, to save the student the superman must have velocity equal or greater than 91.67 m/s.
Note: - It is assumed that the acceleration due to gravity is uniform on the surface of the earth.
- It is assumed that the air resistance is negligible.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)