Solving for Boat Movement with Vectors: Direction and Speed in a Current

[terainfizik]

Homework Statement

A boat needs to sail due north , but the current is flowing southeast at a speed of 20km/hr. In still wate, the boat has a maximum speed of25km/hr .

(a) In what direction will the boat actually move (relative to an observer on land)?

(b) What's the course (direction) necessary to that ship could travel North ?

(c) What is the speed of the boat relative to an observer on land?

Homework Equations

N/A

The Attempt at a Solution

(a) North .

(b) East . I using vector theory .

(c) Using theorem phythogoras :

Speed^2 = 25^2 - 20^2
= 225
speed = 15 km/hr



Am I correct ? PLease give me the answer .

 

[tiny-tim]

No.

As you know, Pythagoras' theorem only works for right-angled triangles, and you don't have a right-angled triangle here.

You only know two directions and two lengths and the angle between them. That gives you a triangle for (a) and another one for (b).

Draw the triangles (only roughly - I'm not suggesting you measure them!), to make sure you've got them the right way round.

Then use sines or cosines to work out the unknown length and the unknown angle!

 

[HallsofIvy]

Remember that the "sine law" and "cosine law" let you use sine and cosine on non-right triangles. As tiny-tim said, start by drawing a picture and identifying the parts of the triangle.