What's the Correct Way to Add Multiple Vectors Using Components in Physics?

[quis]

hey, I've just started physics (yr 11&12 by distance education) and already stuck. So the very basic Question is:
When working out multiple vectors, I understand that it is necessary to break them down into components. (I've been taught to graph the x component and y component for each vector and then add all the x components, ad all the y components then R=square root of (x^2+y^2))
However I keep coming up with the wrong answer for this problem:
A cyclist undergoes three successive displacements of 120m at N40E followed by 82m at S72E and finally 195m at S35W. (all in degrees)
The answer is 102.7m at S24.9E
but I get 120.4m at S69.3W? What have I done wrong?.

 

[ZapperZ]

hey, I've just started physics (yr 11&12 by distance education) and already stuck. So the very basic Question is:
When working out multiple vectors, I understand that it is necessary to break them down into components. (I've been taught to graph the x component and y component for each vector and then add all the x components, ad all the y components then R=square root of (x^2+y^2))
However I keep coming up with the wrong answer for this problem:
A cyclist undergoes three successive displacements of 120m at N40E followed by 82m at S72E and finally 195m at S35W. (all in degrees)
The answer is 102.7m at S24.9E
but I get 120.4m at S69.3W? What have I done wrong?.

We can't figure out what you did wrong if you don't show your work. Write out explicitly the x and y components that you summed up.

Zz.

 

[quis]

Details of working

sure, sorry, new to this.
A cyclist undergoes three successive displacements of 120m at N40E followed by 82m at S72E and finally 195m at S35W.
Vetor::::::X component ::::::::::: Y Component
120m:::120 cos 40 = 91.9 ::::: 120 sin 40 = 77.13 (ie NE)
82m::::82 cos 72 = 23.3 :::::: 82 sin 72 = (-)77.98 (ie SE )
195m:::195 cos 35 =(-)159.7:: 195 sin 35 = (-)111.8 (ie SW)
R ::::::: =(-)44.5 ::::::::::::::::: = (-)112.65
R= square root of (44.5^2+112.65^2) = 121.1
angle=tan(-1)(112.65/44.5) = 68.4
(The answer in the back of the pamphlet is 102.7m at S24.9E)

 

[ZapperZ]

sure, sorry, new to this.
A cyclist undergoes three successive displacements of 120m at N40E followed by 82m at S72E and finally 195m at S35W.
Vetor::::::X component ::::::::::: Y Component
120m:::120 cos 40 = 91.9 ::::: 120 sin 40 = 77.13 (ie NE)
82m::::82 cos 72 = 23.3 :::::: 82 sin 72 = (-)77.98 (ie SE )
195m:::195 cos 35 =(-)159.7:: 195 sin 35 = (-)111.8 (ie SW)
R ::::::: =(-)44.5 ::::::::::::::::: = (-)112.65
R= square root of (44.5^2+112.65^2) = 121.1
angle=tan(-1)(112.65/44.5) = 68.4
(The answer in the back of the pamphlet is 102.7m at S24.9E)

Sorry, I forgot that I attempted this. That's what happens when you get old - you forget things.

Now, there is a problem at my end in understanding the notation being used. What does N-angle-E mean? To me, N40E seems to indicate that the direction is 40 degrees to the east of north.

The same with all the other directions given. If this is true, then it doesn't match the components you have written.

Zz.

 

[quis]

Thanks for following up,
yeh it's the compass system, that is how it's written in my textbook.
so if that don't match the components I've written does that mean that I've got then the wrong way around, I mean using Cos and sine at the wrong times? please explain.