Question

A swimmer wishes to cross a 500m wide river flowing at 5 km/h. Its speed with respect to water is 3 km/h. It he heads in a direction making an angle $\theta$ with the flow, the time he takes to cross the river and shortest possible time to cross the river is

• A. $\frac{15min}{cos\theta },10min$
• B. $\frac{15min}{sin\theta },10min$
• C. $\frac{10min}{sin\theta },10min$
• D. $\frac{10min}{cos\theta },10min$

Answer 1

The correct option is C $\frac{10min}{sin\theta },10min$

$\begin{array}{c}V=3\sin \varnothing \\ S=0.5KM\\ T=\frac{0.5}{3\sin \varnothing }hours=\frac{10}{\sin \varnothing }min\end{array}$

Vertical componenet to opposite side $=3KM/hr$

$T=\frac{0.5}{3}=0.16hr=10min$