A rowboat crosses a river with a velocity of 3.30 mi/h at an angle 62.5° north of west relative to the water. the river is 0.505 mi wide and carries an eastward current of 1.25 mi/h. how far upstream is the boat when it reaches the opposite shore?

Rowboat arrives 0.558 miles to the upstream when it reaches the opposite shore.

Explanation:

Velocity of rowboat = 3.30 mi/h

Angle with north of west = 62.5⁰

Width of river = 0.505 mile.

Velocity of river = 1.25 mi/hr eastward.

Let us take east as positive X - axis and North as positive Y-axis.

So angle of boat with horizontal axis = (90+62.5) = 152.5⁰

Horizontal speed of boat = 3.30*cos 152.5 = - 2.93 mi/h

Vertical speed of boat = 3.30*sin 152.5 = 1.52 mi/h

Horizontal speed of river = 1.25 mi/h

Time taken to cross river = Width of river/Vertical speed = 0.505/1.52 = 0.33 hour.

Velocity along upstream of river = - 2.93+1.25 = - 1.68 mi/hr

So distance moved along upstream = - 1.68*0.33 = - 0.558 miles (negative sign means along west direction)

It reaches 0.558 miles to the upstream when it reaches the opposite shore.