Question

A body is thrown vertically upward with velocity $u$, the greatest height h up to which it will rise is \[h=\dfrac{{{u}^{2}}}{2g}\]
\[\begin{align}
  & A.\dfrac{u}{g} \\
 & B.\dfrac{{{u}^{2}}}{2g} \\
 & C.\dfrac{{{u}^{2}}}{g} \\
 & D.\dfrac{u}{2g} \\
\end{align}\]

Answer 1

Hint: The newton’s third equation of motion has been used to solve the question.
That is written as,
\[{{v}^{2}}={{u}^{2}}+2as\]
In which \[v\] is the final velocity with which body travels, \[u\] is the initial velocity with which body travels,\[a\] is the acceleration taking place and \[s\] is the distance travelled of the body. These specific terms can be replaced using the appropriate terms when the motion is in free fall. These all may help us to solve this question.

Complete step-by-step answer:

Here, according to newton’s third equation of motion, we can write that,
\[{{v}^{2}}={{u}^{2}}+2as\]
Here the final velocity with which the body is being finally found is considered to be zero when the object reaches its maximum height. Therefore we can write,
\[v=0\]
The acceleration of the body will be equal to the acceleration due to gravity as it is a free fall.
\[a=-g\]
And also the distance the body will travel will be equal to the maximum height.
\[s=h\]
Substituting these all in the equation of motion will give,
\[{{0}^{2}}={{u}^{2}}-2gh\]
Rearranging the terms will give,
\[h=\dfrac{{{u}^{2}}}{2g}\]

So, the correct answer is “Option B”.

Note: In mechanics, free fall is referred to as any motion of a body occurring where gravity is the only force experiencing upon it. According to the concepts of relativity in which gravitation is indicated to a space-time curvature, the body in free fall will be having no force experiencing on it. In the space or vacuum where there are no free air molecules or supportive surfaces, the astronauts are only experienced upon by gravity. Therefore they are coming towards Earth at the acceleration of gravity.