Question

Tarzan and Jane have an argument and aimultaneoualy walk away from where they were atanding. Tarzan atompa off for 42 metera in a direction 50 weat of north and then atopa. Jane walka 24 metera in a direction 80° south of eaat and then atopa. After aome aulking, Tarzan realizea he waa at fault and turna to face Jane. 9. a. Draw a veotor addition diagram for thia aituation to some relative scale. b. How far must Tarzan walk in a straight line to get to Jane? Sohve thia queation using vector addition and vector componenta. Show all atepa. Anawer: 62.3 m c. In what direotion muat he walk? Anawer: 54.3° south of eaat.

Answer 1

The situation given in the problem is shown below.

  

N: North 42 m、 50 x E : East W : West 80° 24 m S: South

Figure : 1

The path of Tarzan is shown by vector A ( here, the direction of Tarzan is shown towards the Jane )and the path of Jane is shown by vector B .

(a) The vector addition diagram is shown below :

  

  Figure : 2

This diagram is just for better understanding.

Here vector R is showing the resultant vector.

or,   R = A + B

(b)  From figure : 1 , we can write

or,   

And,   

or,   

So,   

or,   

So, the magnitude of R is

  

Hence, Tarzan must have to walk 62.3 m in a straight line to get Jane.

(c) The direction or the angle made by resultant vector R with positive x - axis can be calculated as

hence, he should walk in a direction 54.3⁰ south of east .

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