Question

the width of the river.

Answer 1

Minimum time taken to cross the river $t_1=600$ s
Minimum time taken $t_1=10$ min $=600$ s

Time taken (for shortest distance ) $t_2=12.5$ min $=750$ s

$\therefore$ Width of the river $d=V_{MR}{t}_1$ ............(1)

Also $d=V_{MR}sin\theta$ $t_2$ ............(2)

From (1) and (2), $V_{MR}{t}_1=V_{MR}sin\theta$ $t_2$

$\therefore$ $600=sin\theta \left(750\right)$ $⟹sin\theta =0.8$ OR $\theta ={53}^o$

For shortest distance, $V_{MR}cos\theta =V_R$

where Horizontal drift $BC=120$ m

Time taken $t_1=10$ min $=600$ s

$\therefore$ $BC=V_R{t}_1$

OR $120=V_R\left(600\right)$ $⟹V_R=0.2$ m/s

$\therefore$ $V_{MR}cos\left({53}^o\right)=0.2$ $⟹V_{MR}=0.33m/s$

Using $d=V_{MR}{t}_1$

$\therefore$ $d=0.33\times 600=200$ m