Question

When two bodies move uniformly towards each other, the distance between them diminishes by $16\text{m}$ every $10\text{s}$. If bodies move in same direction with velocities of the same magnitude as before, the distance between them will decrease by $3\text{m}$ in every $5\text{s}$. The speed of each body is

• A. $1.5\text{m/s}\text{and}0.8\text{m/s}$
• B. $1.1\text{m/s}\text{and}0.5\text{m/s}$
• C. $2.4\text{m/s}\text{and}1.5\text{m/s}$
• D. $3.0\text{m/s}\text{and}1.5\text{m/s}$

Answer 1

The correct option is B $1.1\text{m/s}\text{and}0.5\text{m/s}$

Let velocity of bodies be $v_1$ and $v_2.$
In first case, relative velocity
$u_1=v_1+v_2....\left(i\right)$
In second case, relative velocity
$u_2=v_1-v_2......\left(ii\right)$
$\therefore v_1=\frac{u_1+u_2}{2}$ and $v_2=\frac{u_1-u_2}{2}$
Here $u_1=\frac{16}{10}\text{m/s}$ and $u_2=\frac{3}{5}\text{m/s}$
After solving we have
$v_1=1.1\text{m/s}$ and $v_2=0.5\text{m/s}$