Solving Vectors Question: Mountain Rescue Post O Receives Distress Call

[turnstile]

A mountain rescue post O receives a distress call via a mobile phone from a walker who has broken a leg and cannot move. The walker says he is by a pipeline and he can also see a radio mast which he believes to be south-west of him. The pipeline is known to run north-south for a long distance through the point with position vector 6i km, relative to O. The radio mast is known to be at the point with position vector 2j km, relative to O.
(a) Using the information supplied by the walker, write down his position vector in the form (ai + bj).

The rescue party moves at a horizontal speed of 5 km h-1. The leader of the party wants to give the walker and idea of how long it will take to for the rescue party to arrive.
(b) Calculate how long it will take for the rescue party to reach the walker’s estimated position.

The rescue party sets out and walks straight towards the walker’s estimated position at a constant horizontal speed of 5 km h-1. After the party has traveled for one hour, the walker rings again. He is very apologetic and says that he now realizes that the radio mask is in fact north-west of his position
(c) Find the position vector of the walker.

(d) Find in degrees to one decimal place, the bearing on which the rescue party should now travel in order to reach the walker directly.

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If you've helped me before... you'd know that I explain what i plan to do with the question and whether or not i have it right... but this one .. i have absolutely no clue

i can get as far as drawing the diagram of 6 units in the x-axis and 2 units in the y axis...

please help...

 

[Hootenanny]

Hi turnstile,

So, if you have drawn your graph correctly you should have a point at (0,2) and a line at i =6, yes? Now, draw a right angled triangle, with the hypotenues extending from the point (0,2) to the line i = 6, and the base horizontal from the point (0,2) to the line i = 6. The walker states that the radio mast (0,2)is south west from him, which means your hypotenues should make an angle of 45 degs with the vertical line i = 6.

Does that help any?

~H

 

[turnstile]

Hi hootenanny..

i get what you've just said... and that was what i set out to do...

but my markscheme has a diagram version i do not understand...

i get the 2j and 6i lines above... but what have the done to the rest ?

 

[nrqed]

Hi hootenanny..

i get what you've just said... and that was what i set out to do...

but my markscheme has a diagram version i do not understand...

i get the 2j and 6i lines above... but what have the done to the rest ?

w1 is where they initially think the guy is (he says the mast is southwest from him). The rescuers walk in that direction and they are at th epoint marked R when he calls them and now they realize that he is in fact at w2 (so the mast is northwest of him).



For part a), notice that the vector going from th emast to w1 is at 45 degrees, so it is 6 i + 6 j. It is now easy to answer part a)

 

[turnstile]

ah... so 6i+6j+2j = 6i+8j ?

 

[nrqed]

ah... so 6i+6j+2j = 6i+8j ?

yes. Indeed.

 

[turnstile]

The rescue party moves at a horizontal speed of 5 km h-1. The leader of the party wants to give the walker and idea of how long it will take to for the rescue party to arrive.
(b) Calculate how long it will take for the rescue party to reach the walker’s estimated position.

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i guess i have to find the length OW1 and then divide that by 5...
but how to find this length? :S

 

[nrqed]

The rescue party moves at a horizontal speed of 5 km h-1. The leader of the party wants to give the walker and idea of how long it will take to for the rescue party to arrive.
(b) Calculate how long it will take for the rescue party to reach the walker’s estimated position.

---
i guess i have to find the length OW1 and then divide that by 5...
but how to find this length? :S

It is really weird that they talk about a "horizontal speed". That makes no sense but it woul dmake the calculation very easy. Just take the horizontal distance and divide by 5!

(but the length OW1 is easy once you know the vector from O to w1! Use Pythagora's theorem!)