Can someone explain step by step how to solve?

Question

A cruise ship is traveling south, approximately 22mph when it hit a gulf stream flowing east of 4mph

A)what is the vector component for the cruise ship?(show work

B)what is the vector component for the Gulf Stream?(show work)

C)what is the resultant vector?(show work)

D)find the resultant velocity.round to the nearest tenth(show work)

Answer 1

If the ship is travelling south at a speed of 22mph, that means it's going at a direction of 270° with a magnitude of 22. Also, the gulf traveling east at a speed of 4mph means it's going at a direction of 0° with a magnitude of 4. We can represent these objects as vectors:

Ship:〈22cos270°,22sin270〉= 〈22(0),22(-1)〉=〈0,-22〉

Gulf:〈4cos0°,4sin0°〉= 〈4(1),4(0)〉= 〈4,0〉

The resultant vector will be the sum of the horizontal and vertical components of the vectors:

Ship + Gulf =〈0,-22〉+〈4,0〉=〈0+4,-22+0〉=〈4,-22〉

Also, the resultant velocity can be determined by finding the magnitude of the resultant vector:

||Ship+Gulf|| = √(4²+(-22)²) = √(16+484) = √500 = 10√5 ≈ 22.4mph

Hope this helped!

Answer 2

ship: <0i, -22j>

wind: <4i, 0j>

s + w = (0i, -22j> + <4i, 0j>

|| s + w ||² = 4² + (-22)²