Question

Two swimmers $A$ and $B$ start swimming from different position on the same bank as shown in figure. The swimmer $A$ swims at angle ${90}^{\circ }$ with respect to the river to reach point $P$. He takes $120$ second to cross the river of width $10\text{m}$. The swimmer $B$ also takes the same time to reach the point $P$

• A. Velocity of $A$ with respect to river is $\frac{1}{6}\text{m/s}$.
• B. River flow velocity is $\frac{1}{4}\text{m/s}$.
• C. Velocity of $B$ along y-axis with respect to earth is $\frac{1}{3}\text{m/s}$.
• D. Velocity of $B$ along x-axis with respect to earth is $\frac{5}{24}\text{m/s}$.

Answer 1

Answer: (B), (D)

The correct options are
B River flow velocity is $\frac{1}{4}\text{m/s}$.
D Velocity of $B$ along x-axis with respect to earth is $\frac{5}{24}\text{m/s}$.

Velocity of river flow-
$V_r=\frac{d}{t}=\frac{30}{120}=\frac{1}{4}\text{m/sec}$
Velocity of $A$
$V_A=\frac{d}{t}=\frac{10}{120}=\frac{1}{12}\text{m/sec}$
Velocity of $A$ wrt river
${\overrightarrow{V}}_{Ar}={\overrightarrow{V}}_B=\frac{1}{12}\hat{j}-\frac{1}{4}\hat{i}$
$|V_{Ar}|=\sqrt{\frac{1}{144}+\frac{1}{16}}=\sqrt{\frac{10}{144}}\text{m/s}$

For (B)
Velocity of B along $x$ direction
$V_{Bx}=\frac{25}{120}=\frac{5}{24}\text{m/s}$
Velocity of B along $y$ direction
$V_{By}=\frac{10}{120}=\frac{1}{12}\text{m/s}$