A river 500 ft wide flows with a speed of 8 ft/s with respect to the earth. A woman swims with a speed of 4 ft/s with respect to the water.
1) If the woman heads directly across the river, how far downstream is she swept when she reaches the opposite bank?
d1 =
2) If she wants to be swept a smaller distance downstream, she heads a bit upstream. Suppose she orients her body in the water at an angle of 37° upstream (where 0° means heading straight accross, as in part (a)), how far downstream is she swept before reaching the opposite bank?
d2 =
3) For the conditions of part (b), how long does it take for her to reach the opposite bank?
t =

1)

2)  

3)

Explanation:

Given:

width of river,

speed of stream with respect to the ground,

speed of the swimmer with respect to water,

Now the resultant of the two velocities perpendicular to each other:

Now the angle of the resultant velocity form the vertical:

so,

Now the distance swept downward:

2)

On swimming 37° upstream:

The velocity component of stream cancelled by the swimmer:

Now the net effective speed of stream sweeping the swimmer:

The  component of swimmer's velocity heading directly towards the opposite bank:

Now the angle of the resultant velocity of the swimmer from the normal to the stream:

Now the distance swept downstream:

3)

Time taken in crossing the rive in case 1:

Time taken in crossing the rive in case 2:

b.

explanation: