Draw a diagram to scale showing the direction in which a man must row across a river in order to reach a point directly opposite, if he rows 3 mile/hr while the speed of current is 2 mile/hr.

Question

My ans- with angle of 33' with straight line he wants to travel. And V=3.6 mile/hr.

Now if the river is 1/4 mile broad, how long does it take to cross it and what is the velocity of the boat relative to the shore.

Is this correct?
ans- 3.6 mile in 1 hr then for 0.25 mile t=4.16 min. And relative velocity is 3.6 mile/hr.

Answer 1

3 sin thete = 2
theta = 41.81

V across = 3 cos theta
= 2.24 mi/hr

(1/4)/2.24 = .112 hr = 6.7 minutes

He has zero velocity parallel to the shore (that is the whole point)
However he has speed of 2.24 mi/hr perpendicular to the shore.