Question

A stone is thrown vertically upward with an initial speed $u$ from the top of a tower and reaches the ground with a speed $3u$, then the height of the tower is
(A) $\dfrac{{3{u^2}}}{g}$
(B) $\dfrac{{4{u^2}}}{g}$
(C) $\dfrac{{6{u^2}}}{g}$
(D) $\dfrac{{9{u^2}}}{g}$

Answer 1

Hint Here, find the initial and final velocity of the stone and substitute the values in the equation of motion to determine the value of height of the tower.

Formula Used: Here we will be using the one of the equations of motion, the expression for final velocity is ${v^2} = {u^2} + 2gh$, where $v$ is the final velocity, $u$ is the initial velocity, $g$ is the acceleration due to gravity and $h$ is the height of the tower.

Complete step by step solution
Let the height of the tower be $h$.
Assume the throw in upward direction as positive and downward direction as negative.
The given initial speed of the stone thrown vertically upwards is $u$.
The velocity with which the stone reaches the ground is the final speed of the stone and the given value of final velocity is $3u$.
The expression for final speed reached by the stone from the equations of motion is,
$\Rightarrow {v^2} = {u^2} + 2gh$
Substitute $3u$ for $v$, $u$ for $u$ and $h$ for $h$ in the above expression.
$\Rightarrow {\left( {3u} \right)^2} = {\left( u \right)^2} + 2gh$
Now, write the square of the values and then take the same variable to one side.
$\Rightarrow 9{u^2} - {u^2} = 2gh$
Subtract the value at the right hand side of the equation and divide both sides of the expression by $2g$ to determine the value of height.
$\Rightarrow \dfrac{{8{u^2}}}{{2g}} = h$
Rearrange and reduce the equation.
$\Rightarrow h = \dfrac{{4{u^2}}}{g}$

So, option $\left( B \right)$ is correct answer

Additional information:
Motion is defined as the change in position of an object with respect to time. It is a change in position based on the reference point of an individual. In physics, equations of motion are explained as the behaviour of the physical system in terms of motion. There are three equations of motion to determine the components such as displacement, velocity, distance and time.

Note
Assumption of direction is necessary, that is, upward direction as positive and downward direction as negative. Determination of Initial and final velocity is required if not mentioned in the question.