Question

A freely falling body has a velocity V after falling through a distance h. The distance it has to fall down further for its velocity to become 2V is :

• A. 3h
• B. 2h
• C. h
• D. 4h

Answer 1

The correct option is (A) 3 h

Step 1, Given data

The initial speed of the body $u=0$

Acceleration of the freely falling body $a=g$

Velocity of body after covering $h$ distance, $v_1=V$

Step 2,

From the third equation of motion

We know

$v^2-u^2=2gh$

Putting all the values

$\therefore$ $V^2-0=2gh$

We get $V^2=2gh$ ....(1)

Let the total distance covered by body to attain $v_2=2V$ be $H$.

We know from the equation of motion

$v^2-u^2=2gh$

Putting all the values

Or $4V^2-0=2gH$

Or $4V^2=2gH$

Or $4\left(2gh\right)=2gH$

Thus we get $H=4h$

Now required distance the body needed to fall $\Delta h=H-h$

$\therefore$ $\Delta h=4h-h=3h$

Hence the correct option is (A)