A sailboat runs before the wind with a constant speed of 4.5 m/s in a direction 33 ° north of west. How far west has the sailboat traveled in 27 min?

Question

I don't understand what formula to use for this kind of problem. As well as I don't understand which variables already exist in the problem. Please help

Answer 1

The 4.5 m/s is the speed of the boat along its travel direction.

Think of the travel path as being the hypotenuse of a triangle, that 4.5 m/s can be broken into a speed along the west leg of the triangle and a speed along the north leg of the triangle.

 

Since the boat is pointing 33 degrees north of west, its path makes an angle of 33 degrees to the west direction (I picture "west" as going to the left.)

That means that the speed of the boat along the west direction, S_W, is related to the speed of the boat (along the hypotenuse), S, by:

 

S_W = S * cos(33)

      = 4.5 * 0.8387

       = 3.774 m/s

 

So the westerly distance travelled in 27 minutes is:

 

d_W = 3.774 * 27 * 60   <-- 60 seconds per minute

      ~ 6114 meters, or 6.114 km

 

    Diagram:     "\" = path of the Boat

 

North

|

|    \

|        \ 

|             \  

|                   \

|                         \

|               33 deg      \

____________________Boat   

                     <--West      East-->

 

Jez: I'm in Holyoke in case you ever want to do some in person or online tutoring  ;-)