Applied Maths - Relative velocity - Quick question

Prodigious

Hey all,
Doing a bit of revision and stuck on a question...

Fundamental applied Maths edition 2, pg 56 q 8

If anyone could give me advice it would be great

If you don't have the book and can help I'll write out the question..
Thanks

Apocladagr0

Im presuming you're comfortable calculating the rel. velocity V_AB, and bringing A towards the junction. If you're not I'll explain.

once you've done that:

Bring A towards the junction, so that B is on a horizontal line so that [AB] = 762.5 m.

find the direction of V_AB, which should come out as tan(theta) = (2sqrt(3))/7
now figure out cos(theta), using pythagoras. ( = 7/sqrt61)

Then, using similar triangles,

cos(theta) [a distance along v_ab] = x/762.5 m

==> x/762.5 = 7/sqrt61

x = 683.4

T = rel. dist/rel. speed

so x/ | V_AB | = 21.875

but this is the time since they were side by side since they were at the junction (which we did to make the Q easier, wasn't the original way the Q was asked) so we have to subtract it from the amount of time it took A to get to the junction, 28.125.

= 6.25s

(ii)

|AO| = 450 − 16t

|BO| = 200 + 20t

they're equal, so solve for t:

==> t = 6.94s


Sorry, its a bit rushed but if you don't get my solution I'll redo it:cool:

ps. part (i) took me absolutely ages about 2 weeks ago, should have had some extra help in the book I think.

Prodigious

Fair play man thanks a mill

I'm obviously a bit slow... Stuck on getting the direction of V.ab ...

V.ab = -28i - 13.856j. So I would normally go with Tan(Theta) = 13.856/28

Where am I going wrong?

Apocladagr0

Yep thats right, 13.856/28 = 2sqrt(3)/7

draw a triangle with those as opp & adj sides, to figure out the hypotenuse and then get cos(theta), so

hyp = sqrt(13.856^2 + 28^2) = 4sqrt(61)

cos(theta) = 28[adj]/4sqrt(61)[hyp]

that triangle is similar to the one with x and the rel. distance, so we can solve for x by letting

x/762.5 equal 28/4sqrt(61)

I still find it confusing to figure out, had to get my copy

Prodigious

Brilliant stuff thanks again, sorted now

aarond280

just wondering if you know how to do the relative velocity question 2009 2(b) HL, thanks