Awoman can row a boat at 4.0 mph is still water.
1. if she is crossing a river where the current is 2.0 mph, in what direction must her boat be headed if she wants to reach a point directly opposite her starting point?
2. if the river is 4.0 mi wide, how long will it take her to cross the river?

1) from the positive x-axis.

2)

Explanation:

Given:

speed of rowing in still water,

1)

speed of water stream,

we know that the direction of resultant of the two vectors is given by:

where:

the angle of resultant vector from the positive x-axis.

angle between the given vectors

When the rower wants to reach at the opposite end then:

so,

from the positive x-axis.

2)

Now the resultant velocity of rowing in the stream:

Therefore time taken to cross a 4 miles wide river:

snell's law

refractve index = sin incidence / sin refraction