Question

When two bodies $A$ and $B$ move uniformly towards each other, the distance between them diminishes by $16m$ every $10s$. If velocity of body $B$ is reversed, the distance between them will decrease $3m$ every $5s$. The magnitude of velocity of $B$ is $\frac{10}{x}m{s}^{-1}$, then $x$ is

Answer 1

Let $V_A$ be the magnitude of velocity of $A$ wrt ground,
$V_B$ be the magnitude of velocity of $B$ wrt ground,
$V_{AB}$ be the magnitude of velocity of $A$ wrt $B$.

When the bodies move toward each other.
$V_{AB}=V_A+V_B$
$\frac{16}{10}=V_A+V_B$
$\Rightarrow V_A+V_B=\mathrm{1.6...........}\left(1\right)$

When velocity of B is reversed , then
$V_A-V_B=\frac{3}{5}$
$V_A-V_B=\mathrm{0.6..........}\left(2\right)$
From (1) and (2)
$2V_B=1$
$V_B=\frac{10}{20}$
$\Rightarrow x=20$