Help with vectors!

[The Rainbow Connection]

Hello everybody! I'm a beginner to physics and I need a bit of help with Vectors. How would you answer this question? I'm unsure what I am really looking for..

A yacht originally moving north at 8kmh^-1 experiences a current of velocity 1kmh^-1 to the north-east. What would be the new velocity of the yacht as the current takes effect?

Thanks

Edited December 2, 2012 by The Rainbow Connection

[Sabs44]

This is just a question of vector addition: if you draw a vector of 8 units North, and then one unit North-east, the final velocity will be the distance from the starting point to the end of these two connected vectors.

Since the current goes 1km/h North East, it can be made up of a (squareroot(0.5)) North vector and a (squareroot(0.5)) East vector...

So the final vector goes 8 + 0.707 = 8.707 km/h North, and 0.707 km/h East.

Using Pythagoras' rule, the final velocity = square root of [(8.707)^2 + (0.707)^2]

= root of [75.8 + 0.5]

= root [76.3]

= 8.73 km/h

Hope this helps!

Sam.

Edited December 3, 2011 by sabernethy

[The Rainbow Connection]

Thank you very much! I understand everything except why you put 0.5 under a square root sign.. Is it just a formula? Or is there a reason for this?

[Sabs44]

No problem!

And the square root of 0.5 bit is just based off of the vector 1km/h North-east.

You can make a right-angled triangle, with 1 as the hypotenuse. Then if you label the other 2 sides x (since they're the same, since it's a "North-east" vector), you can solve it pretty easily.

Pythagoras':

1^2 = x^2 + x^2

2x^2 = 1

x^2 = 0.5

so x = square root of 0.5

Hope this clarifies things, reply if you need any more help!