Relative Velocity

Y_Shun SG

how you get the 90degree there? i get a 'math error'...

2/sinx = 1.2/sin 36.9

^tamago^ SG

er. move a bit earlier. ignore the right-angle and try to find all the angles involved. see eagle's drawing.

Y_Shun SG

ya i trying to find his red angle, but can't!

^tamago^ SG

er, it's 90º.

actually the main thing is the 53.1º leh. Neutral

Y_Shun SG

but but but...how you get tht 90? >.<
i tot u need to use
180 - 36.9 - 90 = 53.1 ?

lpx88 SG

Using sine rule

But u don use 36.9

Coz its a rounded number

Use yr calculator for atan(30/40) to get 36.8 sth

Use that value for sine rule

lpx88 SG

Final qn..can some1 remind me about the decimal points and sig fig for a maths?

Y_Shun SG

----------- another qtn

absol SG

the new qns like this yr june paper a maths rela velo qns leh
if im nt wrong lol
i try bah...

6(i)
Main point here : when they intersect (thats when the missile hits the spacecraft), their coordinates are the same.

so,

let the time taken from the time when the missile is launched to the time when it hits the spacecraft be t

to find the final coordinates of the spacecraft and missile, u have to take their position vectors plus their speed*time taken. (for spacecraft add 0.5 sec more to time taken since missile was only launched 0.5 sec after it)

SPACECRAFT MISSILE
12j + (t+0.5)(40i + 15j) = 46i + t(ki + 30j)
12j + 20i + 7.5j + (40t)i + (15t)j = 46i + (tk)i + (30t)j
(20+40t)i + (19.5+15t)j = (46+tk)i + (30t)j

19.5+15t = 30t
19.5 = 15t
t=1.3

Therefore, time taken for spacecraft to move across screen before impact = 1.3+0.5 = 1.8s [shown]

(ii)

20+40t = 46+tk
Sub t=1.3
20+52 = 46+1.3k
k = 20

77th Cloud SG

There's a simliar question

(same diagram), which is not drawn to scale, shows a horizontal rectangular surface. One corner of the surface is taken as the origin O and i and j are unit vectors along the edges of the suface.

A bloody fly, F, starts at a point with position vector (i+2j) and crawls across the surface with a velocity of (3i + 2j) cm s-1, At the instant that bloody fly starts crawling, a more bloody spider, S, at the point with position vector (85i + 5j) cm, sets off across the surface wit ha velocity of (-5i + kj)cm/s, where k = constant, given that the bloody insects knock on each other, find k.

heres my working

After t seconds, the bloody fly travels : 3it + 2jt cm
the bloody spider : kjt - 5it

since the spider catches the fly, the distance they travelled after t s is the same

3it + 2jt + i + 12j = 85i + 5j - 5it + kjt
Simplifying, i get : i(8t - 84) = j(-7+kt - 2t)

By whatever rule is that, i forgot, 8t - 84 = 0
t = 10.5
-7 + 10.5k - 21 = 0
k = 8/3

This same method can be applied for the question above, I'll do it if i got time, but i wonder, is it RV or velocity?

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