Answer
Verified
455.7k+ 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
Who among the following was the religious guru of class 7 social science CBSE
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Trending doubts
Derive an expression for drift velocity of free electrons class 12 physics CBSE
Which are the Top 10 Largest Countries of the World?
Write down 5 differences between Ntype and Ptype s class 11 physics CBSE
The energy of a charged conductor is given by the expression class 12 physics CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Derive an expression for electric field intensity due class 12 physics CBSE
How do you graph the function fx 4x class 9 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Derive an expression for electric potential at point class 12 physics CBSE