Answer

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**Hint:**Projectile motion is a form of motion experienced by an object that is projected near the Earth’s surface and moves along a curved path under the action of gravity.

In this question, height and final velocity are given; hence we will find the velocity of projection, then using this velocity of projection, we will find the time.

**Complete step by step answer:**

Given the maximum height reached by the ball h=45m

Let the velocity of projection be u and the final velocity at the top height \[v = 0\]

We know newton law of motion is given as

\[{v^2} = {u^2} - 2gh - - (i)\][ \[ - g\]since the ball is moving in opposition to the direction of gravity]

Here since the final velocity\[v = 0\], so we can write equation (i) as

\[

0 = {u^2} - 2\left( {10} \right)\left( {45} \right) \\

{u^2} = 900 \\

u = 30{\text{ m/sec}} \\

\]

So the velocity of the velocity is \[u = 30{\text{ m/sec}}\]

Now we need to find the time after which the velocity of the ball becomes equal to half the velocity of projection i.e.

\[v = \dfrac{{30}}{2} = 15{\text{ m/sec}}\]

Now use the newton law of motion to find the time which is given as

\[v = u - gt - - (ii)\]

So by substituting the value of velocity, we get

\[

15 = 30 - 10t \\

10t = 15 \\

t = 1.5s \\

\]

Therefore we can say time after which the velocity of the ball becomes equal to half the velocity of projection is\[t = 1.5s\]

Option (B) is correct.

**Note:**Students must know that whenever any object or a particle is moving against the velocity, then its gravity will act in the opposite direction. The projectile has a single force that acts upon it, which is the force of gravity.

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