Question

Suppose you first walk 12.0 m in a direction 200 west of north and then 20.0 m in a direction 40.00 south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position?

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

the compass direction of the resultant displacement is
`\theta  =4.7^o` south of west

Step-by-step explanation:

Generally using cosine we can obtain the resultant R as follows

`R^2  =  A^2  + B^2 -2ABcos(70)`

=>
`R  =  √(12^2  + 20^2  - 2(12 ) *  (20) cos  70)`

=>
`R  =  19.48 \  m`

We can obtain the direction of the resultant by first using sine rule to obtain angle C as follows

`(A)/(sin  C)  =  (R)/(sin70 )`

=>
`C=  sin ^(-1) [(A *  (sin 70))/(R) ]`

=>
`C =  sin ^(-1) [(20 *  (sin 70))/(19.48) ]`

=>
`C =  74.7 ^o`

Then the direction is obtained as

`\theta  =  C  -  70`

=>
`\theta  = 74.7   -  70`

=>
`\theta  =4.7^o`

Hence the compass direction of the resultant displacement is
`\theta  =4.7^o` south of west