If a body is thrown up with an initial velocity u and covers a maximum height

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If a body is thrown up with an initial velocity $u$ and covers a maximum height of $h$ , then $h$ is equal to $\frac{u^{2}}{2 g}$ .

Options:

A . True

B . False

C . It is a scalar quantity.

D . It is always less than or equal to the distance travelled by the object.

Answer: Option A
:
A

Let the initial velocity be $u$ , final velocity be $v$ , acceleration be $a$ and distance covered be $s$ .
Using the equation , $v^{2}$ = $u^{2} + 2 a s$ ,
Here $a = - g$
[ $∵$ acceleration due to gravity is acting opposite to the direction of motion]
$s = h$

At the highest point, $v = 0$

$∴$ $0 = u^{2} - 2 g h$

$\Rightarrow$ $h = \frac{u^{2}}{2 g}$

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