Question

Velocity of the boat with respect to river ($v_{b/r}$) is $10m/s$. It passes the river of width $36m$ and reaches opposite shore at point $R$ shown in the figure. If the velocity of the river is $3m/s$, find the time of the trip and drift of the boat.

• A. $(6s,66m)$
• B. $(6s,60m)$
• C. $(4.5s,49.5m)$
• D. $(6s,49.5m)$

Answer 1

The correct option is A $(6s,66m)$

The given situation can be shown in the figure as below

As per the question, velocity of the boat with respect to river is, $V_b=10m/s$
and, velocity of the river is, $V_r=3m/s$
Hence, time taken by the boat to cross the river is given by,
$t=\frac{d}{V_{by}}=\frac{36}{V_{b}sin{37}^{\circ }}=\frac{36}{10sin{37}^{\circ }}=\frac{36}{6}=6s$
Now, for drift $BC$ we have total velocity in the direction of river flow as
$V_{total}=V_{bx}+V_r=V_{b}cos{37}^{\circ }+V_r$
$⟹V_{total}=10cos{37}^{\circ }+3=8+3=11m/s$
$\therefore$ drift $BC=V_{total}\times t=11\times 6=66m$