When a body is thrown vertically upward with the velocity u you at the greatest height its final velocity will be?

Option 2 : $\frac{{{u^2}}}{{2g}}$

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CONCEPT:

Equation of motion: The mathematical equations used to find the final velocity, displacements, time, etc of a moving object without considering force acting on it are called equations of motion.
These equations are only valid when the acceleration of the body is constant and they move on a straight line.

There are three equations of motion:

V = u + at

V2 = u2 + 2 a S

${\text{S}} = {\text{ut}} + \frac{1}{2}{\text{a}}{{\text{t}}^2}$

Where,

V = final velocity,

u = initial velocity,

s = distance traveled by the body under motion,

a = acceleration of body under motion,

t = time taken by the body under motion.
Explanation:

From the above explanation, we can see that, all motion are governed by laws of motion and in our case when a body is thrown upwards, at the topmost point its final velocity becomes zero

Using the third equation of motion

${v^2} = {u^2} + 2as$

v = 0

a = -g

$- {u^2} = 2\left( { - g} \right)s$

Hence total displacement of the ball will be given as

$s = \frac{{{u^2}}}{{2g}}$

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Question 16 Exercise 3E

Answer:

There will be retardation when a body is thrown vertically upwards having an initial velocity ‘u’ to reach a height ‘h’. The final velocity ‘v’ at the highest point is 0m/s We know from the equation of motion that, $\begin{array}{l} v^{2}=u^{2}-2 g h \\ h_{\max }=\frac{u^{2}}{2 g} \end{array}$

Video transcript

hello everyone welcome to later learning i'm guri your science tutor today's question is a body is thrown vertically upwards with an initial velocity u write an expression for the maximum height attained by the body so let's start our answer when a body is thrown vertically upwards when body is thrown vertically upwards then it experiences retardation and its initial velocity u to reach the height h the final velocity becomes we at highest point is so from the equation of motion that v square is equals to u square minus 2 gh will give you the value of h maximum that is the maximum height which is equals to u square by 2g this is the required expression for more such videos please subscribe leader learning and for any doubts drop a comment thank you

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Answer

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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.