Expert: Paul Klarreich - 2/6/2010

Question
1) A man travelling southward at 15km/h observes that the wind appears to be coming from west. on increasing his speed to 25km/h it appears to be coming from the southwest. find the direction and speed of the wind.

Ans. the wind is coming from a direction 56.18 deg north of west at 18k/hr.

2)A 100kg weight is suspended from the centre of a rope as shown in the adjoining figure. determine the tension in the rope.

Fig.

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\          /            
 \        /               
  \120deg/           
   \    /                
    \  /             
     \/
     |
     |
     |
     |         
  ------
  |100kg|

Ans. 100kg
  ------

pls help me to find the solution

Answer
Questioner: renz
Country: Philippines
Category: Advanced Math
Private: No
Subject: VECTOR
Question: 1) A man travelling southward at 15km/h observes that the wind appears to be coming from west. on increasing his speed to 25km/h it appears to be coming from the southwest. find the direction and speed of the wind.

Ans. the wind is coming from a direction 56.18 deg north of west at 18k/hr.

2)A 100kg weight is suspended from the centre of a rope as shown in the adjoining figure. determine the tension in the rope.

Fig.

--------------
\          /            
\        /               
 \120deg/           
  \    /                
   \  /             
    \/
    |
    |
    |
    |         
 ------
 |100kg|

Ans. 100kg
 ------

pls help me to find the solution


1. From the man's point of view, the wind is first:

A vector pointing east at  A mph.  His southward motion adds an effective 15 mph NORTH to the actual vector of the wind.

so  <Wx, Wy> + <15,0> = <0,A>

Then it is:

A vector pointing Northeast at  B mph.  His southward motion adds an effective 25 mph north to the actual vector of the wind.

so  <Wx, Wy> + <25,0> = <B,B>

I think now we have enough info:

Wy = A
Wx + 15 = 0,  so  Wx = -15,  which is 15 mph from the south.

Wx + 25 = B = Wy

-15 + 25 = Wy

Wy = 10, which is 10 mph from the West.

You can do the rest.

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2. If you mean the bottom piece of rope, it is simply the mass it supports, I think.