In which direction will the ferry actually travel? How fast will it travel?

Question

The ferry heads west across a river. It travels at 20 miles per hour in still water. The river flows south at 15 miles per hour.

Answer 1

You can add velocity vectors to obtain a resultant velocity...a velocity has speed and direction.

Draw the following diagram.  An arrow beginning at A pointing left on the page which we can call west with measure labeled 20 and ending at B.  This vector AB represents the velocity of the ferry without flow.  Now draw a vector BC with measure 15 down the page (south) and perpendicular to AB so that it represents the river flow.

 

The resultant is AC (arrow points at C) which represents the actual speed and direction (velocity) of the boat.

To calculate the speed look at diagram and use Pythagoras' Th.  To calculate direction you can express as an angle from west...use inverse trig function..(you know 2 sides of a right triangle ABC).