Amaths help please

Evo4eva SG

Ermm...can anyone help me on the the topic relative velocity in AM.
I need help knowing how to draw the diagram Embarassed l0l...
like they always say the wind is blowing 050 bearing from smthsmth
can somebody explain how to draw pls?....sry i m unable to give any question,donno what to give...l0l...

unclebutcher SG

050 bearing means, from the vertical line(north) you measure 50 degrees and draw a line

^tamago^ SG

u noe vectors?

Evo4eva SG

o.o...
ya,i know vectors..
since no question very hard to help,i put some question..
Q: A town A is 320km due west of a town B. On a day when there is no wind an aircraft takes 50min to fly from A to B. On a second day, when the wind is blowing from a direction 350, the aircraft also takes 50min for the journey from A to B.Find
a)the course set by the polot on this second day,
b)the speed,in km/h,of the wind..
thx for the help,best got diagram if possible..hahaha,i need to learn the diagram to solve the question.

^tamago^ SG

some variables are missing. what is the speed of the wind? Confused

cos if no wind and got wind also takes the same time, then the air speed and resultant velocity should be the same.

angelfairy SG

y not?

anyway no answers? like maybe 070 and 133.4

Evo4eva SG

l0l...dunno,the question from TYS,oso nv stat wind speed....
another question then..
Q:A motor boat travels in a straight line across a river which flows at 3m/s between straight parallel banks 200m apart. The motor boat, which has a top speed of 6m/s in still water, travels directly from a point A on one bank to a point B,150m downstream of A, on the opposite bank. Assuming that the motoring boat is travelling at top speed, find, to the neareset second, the time it takes to travel from A to B

lpx88 SG

Sorry hijack thread for a while ah

For differentoation of 1/cosX

do we re-express it as cosX^-1 and do normal differentiation or we have to use quotient rule?

^tamago^ SG

can same time, but.......

angelfairy SG

1/cosx is just secx, differentiate is just secxtanx

^tamago^ SG

d/dx(sec x)

use quotient rule.

lpx88 SG

Qn at first is secx....but tys nvr say d/dx secx gives us what..so i converted it to 1/cosX? Shocked

angelfairy SG

then do as tamago said, btw for the diagram i got the same one as yours except my internal angle is 80 not 100...

Evo4eva SG

o.0...u got the answer.
a)070
b)133km/h
how u get?...l0l.....
can explain how u get the diagram,sry,i really suck at maths.

lpx88 SG

With Pythagoras theorem find distance the boat will travel

Then, find angle X. U can find this by using sohcahtoa(sin = oppo/hyp..bla bla), then use 90 degrees, minus off this angle u just found. Answer u get will be angle X

Use sine rule and get angle B

180 degrees - angle X - angle B= Angle Z

With angle Z, u can use sine rule or cosine rule to get final velocity

Dist/ Velocity = time

^tamago^ SG

changed cos direction of travel shld be east.

v² = (384km/h)² + (384km/h)² - 2(384km/h)(384km/h) cos 20º
v = 133.7km/h

lpx88 SG

X2....Then jus use sine rule can get answer liao..

^tamago^ SG

sin a = 200/250 = 0.8
6/sin a = 3/sin b
sin b = 0.5×0.8=0.4
Z = 180º - asin(0.8 ) - asin(0.4) = 103.3º
v² = (3m/s)² + (6m/s)² - 2(3m/s)(6m/s) cos 103.3º
v = 7.30m/s

t = (250m)/(7.30m/s) = 34s (nearest sec)

Evo4eva SG

Very Happy thx thx for all ur help..

tanjun SG

Last time, I ask my school teachers about this. They give me a straight "no".
Never write cos^-1 x in your ans. Rewrite it as sec x. or write it as (cos x)^-1
They give me a reason that cos^-1 x will be misunderstood by them as arc cosine x which represents the inverse function of cosine as this symbol is commonly used by the calculator. Many students are misunderstood due to the confusion of these symbols sin^-1, cos^-1, tan^-1.

If you want to express 1/cos x in a simpler way, they say just simply put sec x or (cos x )^-1