Question

A fisherman wishes to travel due north M in order to cross a river 3km flowing due east at 2km/hr. if it can roll at 8km.hr in still water, calculate a)the direction in which it must head its boat in order to get his destination direct opposite the starting point
b)resultant velocity of boat in the river
c)time taken to cross the river

Answer 1

Answer on Question #79865, Physics / Mechanics | Relativity

Question:

A fisherman wishes to travel due north M in order to cross a river $3\mathrm{km}$ flowing due east at $2\mathrm{km/hr}$ . if it can roll at $8\mathrm{km/hr}$ in still water, calculate a) the direction in which it must head its boat in order to get his destination direct opposite the starting point

b)resultant velocity of boat in the river

c)time taken to cross the river

Solution:

The movement should be done under the angle $\alpha$ with respect to the line of the river so $\nu_{B}\cos \alpha = \nu_{r}$ , where $\nu_{B}$ is boat velocity, $\nu_{r}$ - velocity of the river. Then $\alpha = \arccos \frac{2}{8} = 75.6{}^{\circ}$ . Respectively crossing time $\tau = \frac{l}{\nu_{2}} = \frac{l}{\nu_{B}\sin\alpha} = \frac{3}{8\sin 75.6} = 0.39\mathrm{hr}$ . Velocity of boat in the river $\mathbf{v} = \mathbf{v}_{2} = 7.8\mathrm{km / hr}$ .

The answer:

a) direction $\alpha$ is $75.6{}^{\circ}$

b) resultant velocity of boat in the river is $7.8\mathrm{km / hr}$ .

c)time taken to cross the river is $0.39\mathrm{hr}$

Answer provided by https://www.AssignmentExpert.com