Soto family is rafting across the river.

Stretch of the river is meter wide and the river is flowing south at a rate of .

In still water raft travels .

(a)

Speed of the raft is represented by the resultant vector .

Draw the diagram for the current situation:

The resultant vector is the sum of the vectors representing the path of the raft and the vector representing

flow of the river .

The component form of the vectors and .

From the figure,

Find the magnitude of .

 .

Therefore, speed of the raft is about .

(b)

Draw the figure to the corresponding situation for .

Consider down river rafts the land at a distance of meters.

Draw the figure to the corresponding situation.

observe the two triangles in the above figures.

From the property of the similar triangles,

Down river will raft land at a distance of .

(c)

Find the total time taken by Soto family to cross the river:

Find the total distance traveled by the raft:

Draw the figure to the corresponding situation using the result in part (b).

Use the Pythagorean theorem to find the distance .

m.

Speed of the raft is .

.

Substitute and in above expression.

Total time taken by the family to cross the river is .

(a) Speed of the raft is about .

(b) Down river will raft land at a distance of .

(c) Total time taken by the family to cross the river is .