Question

A body is released from a great height, falls freely towards the earth. Another body is released from the same height exactly a second later. Then, the separation between two bodies, $2s$ after the release of the second body is nearly

• A. $15m$
• B. $20m$
• C. $25m$
• D. $30m$

Answer 1

The correct option is C

$25m$

Step 1. Given data:

Time duration of second body freely falling $t=2s$

Since second body is released $1s$ after the release of first body, Total time for which the first body have travelled after the second body travelled for $2s$ is $t=1+2=3s$

Step 2. Solving for Separation between the two bodies

Using newtons equation of motion for a freely falling body

$s=ut+\frac{1}{2}g{t}^2$

Taking $g=10m/s^2$

Where $s$ is the distance travelled, $u$ is initial velocity, $t$ is time taken and $g$ is acceleration due to gravity

For the first body distance travelled $2s$ after the release of the second body is

$$\begin{gathered} s_1=0\times 3+\frac{1}{2}\times g\times {\left(3\right)}^2 \\ =\frac{9g}{2} \end{gathered}$$

For the second body distance travelled $2s$ after the release of the second body is

$$\begin{gathered} s_2=0\times 2+\frac{1}{2}\times g\times {\left(2\right)}^2 \\ =\frac{4g}{2} \end{gathered}$$

The separation is

$$\begin{gathered} d=s_1-s_2=\left(\frac{9}{2}-\frac{4}{2}\right)g \\ =\frac{5}{2}\times 10=25m \end{gathered}$$

Hence, option C is correct