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Further Mathematics Paper 2, Nov/Dec. 2007  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
General Comments
Weakness/Remedies
Strength























Question 17

A body at rest is acted upon by two forces (40 N, 045°) and (θ N, 135°).

(a) Express each of the forces as a column vector.

(b) If the magnitude of the resultant force is 50 N, find the
(i) value of θ;
(ii)) direction of the resultant force, correct to the nearest degree.

_____________________________________________________________________________________________________
Observation

Most candidates did not attempt this number.  Those who did performed woefully exhibiting poor knowledge of Vectors. 

They should understand that the force F2 (40N, 045°)
 
  =     20√2   and F2  =  (θN, 135°) =   {  θ√2 }
         20√2                                            {     2   }
                                                         { -θ √ 2 }
                                                              {         2 }     
 
The resultant R = { 20√2}  +{   ½ (θ√2)}
                               { 20√2}    {− ½ (θ√2)}  and /R/2 =  20√2 + ½ (θ√2)  2 + 20√2 – ½ (θ√2)2                                            

 »  θ   =    30;    tan  x   =    5√2    »  x   =    8.13°  »  8°.
                                                 35√2
  direction of resultant force    =   082°.

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