Question

Two swimmers swim in a stand still lake. First swimmer swims directly across the lake ($30m$ wide) with a velocity of $1.5m/s$, reaches the other end and runs a distance of $10m$ in $10$ seconds along the shore. What should be the velocity of the second swimmer so that he reaches the same point in the same time ?

• A. $(1.5\hat{i}-1\hat{j})m/s$
• B. $(1.5\hat{i}+1\hat{j})m/s$
• C. $(1\hat{i}-1.5\hat{j})m/s$
• D. $(\frac{1}{3}\hat{i}+\hat{j})m/s$

Answer 1

The correct option is D $(\frac{1}{3}\hat{i}+\hat{j})m/s$


Velocity of first swimmer, $v_1=1.5m/s$
Time taken to cover $10m$ along the shore, $t_{QR}=10s$
For the second swimmer to reach the same point in same time, he should cover equal displacement in equal time.
Displacement of first swimmer, $\overrightarrow{S}=10\hat{i}+30\hat{j}$
Time taken by first swimmer to reach the point $R$, $t=t_{PQ}+t_{QR}$
$t=\frac{30}{1.5}+10=30s$
Therefore , velocity of second swimmer, ${\overrightarrow{v}}_2=\frac{\overrightarrow{S}}{t}=\frac{10\hat{i}+30\hat{j}}{30}=(\frac{1}{3}\hat{i}+\hat{j})m/s$