Question

You get in your sailboat and leave the harbor, sailing at 40 degrees south of east for 22 km until you reach a buoy. You circle the buoy and then sail until you are 15 km directly to the north of the point where you first exited the harbor. a) How far have you travelled from the buoy? At what angle relative to south should you look in order to see the buoy?

Answer 1

Answer:33.66 km

Step-by-step explanation:

Given

First sailboat travel
`40^(\circ)` south of east for 22 km to reach the buoy

Position vector of buoy
`r_1`

`r_1=22cos40\hat{i}-22sin40\hat{j}`

Final Position of sailboat
`r_3`

`r_3=15\hat{j}`

from Figure we can say that

`r_1+r_2=r_3`

`r_2=r_3-r_1`

`r_2=15\hat{j}-22cos40\hat{i}+22sin40\hat{j}`

`r_2=-22cos40\hat{i}+29.14\hat{j}`

`|r_2|=33.66 km`

After reaching
`r_3`

`tan\theta =(22cos40)/(29.14)`

`tan\theta =(16.85)/(29.14)`

`\theta =30.04^(\circ)east\ of\ south`