Physics (vectors) question

[Red_x_Lily]

Finally decided to start on my physics hwk, and I got stuck on a question-

A cyclist rides along a straight road for 2.7 km in a direction N 23° E and then 4.3 km along another straight road S 46° E. What is the resultant displacement?

I found the displacement to be 4.17 km (the answer says 4.2, so I guess that’s good enough?), by splitting it into two triangles…I’m not sure if you can do that. When it comes to figuring out the angle, I’m stuck… I’d really appreciate any help! Thanks in advance. 

[cara.mel]

I would encourage your two triangle way =) (you can also draw 1 triangle and use the cosine rule)

I get 4.17km as well, answer is just to 1 dp.
What you do is take the overall displacements west/east (4.14 E) and north/south(0.49 S), draw your triangle (which I assume you did, because you got the right answer ^_^)
Then you use trig again on it from your triangle (tan^-1 4.14/0.49) and you'll get S 83º E

[Red_x_Lily]

Ooh, thank you so much caramel. ^^

[Mao]

as the same for all sciences, always use the lowest number of significant figures

as shown in the question, each value given to you has only two significant figures 2.7 km N 23° E and 4.3 km S 46° E, hence the answer should be answered to two significant figures, 4.2 Km

However, if the lowest significant figures is 3, e.g. 2.70 km N 23.0° E and 4.30 km S 46.0° E, you'll have to answer to 3 significant figures, 4.17 km

in mixed cases take the lowest

hope that helped

PS dont stress too much about it tho, i heard that in a science exam you'll only ever lose max 1 mark if more than half of your answers are not given to the correct sig figs, but if u want as many marks as possible...

[cara.mel]

Physics doesn't care about sig figs, unless you are way out (eg giving 10 when there's 3 in the question, or simplifying it to the point they can't tell if you worked it out or you guessed)
It's chem that's the bitch about sig figs. They will usually pick out 1 or 2 questions before hand and go 'we will mark sig figs on this question, mark states on that one' etc.
But yeah, they only punish you once for mistakes like that

Edit - now I think about it more, I remember in a lot of their assessment reports the answer has more sig figs than the question. 3 is generally a good number to have, which is why I didn't pick up on it

[Red_x_Lily]

I decided the cosine rule is much more convenient. o.o 

Thanks for the info about the sig figures. Can't believe I didn't know about it...lol. It gets kinda annoying though when even the textbook isn't consistent, but I guess it's nothing to fuss about. I generally give my answers to two or three decimal places, or more depending on the question, but now I know what to look out for. And even that one mark can count sometimes...