Question

A body is thrown vertically upward with velocity $u$, the greatest height $h$ to which it will rise is

• A. $\frac{u^{}}{g}$
• B. $\frac{u^2}{2g}$
• C. $\frac{u^2}{g}$
• D. $\frac{u^{}}{2g}$

Answer 1

The correct option is B

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

Step1: Given data

A body is thrown vertically upward with velocity $u$ and the height is given to be $h$.

Step 2: Formula used

Newton’s third equation of motion says that

$v^2=u^2+2as[wherev=finalvelocity,u=initialvelocity,a=acceleration,s=dis\tan cetravelledofthebody]$

Step 3: Calculating height

According to the given data,

1. 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, $v=0$
2. The acceleration of the body will be equal to the acceleration due to gravity as it is a free fall. $a=-g$
3. 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, $h=\frac{u^2}{2g}$

Hence, option B is the correct option.