A cruise ship sails due south at 2.50 m/s while a coast guard patrol boat heads 19.0° north of west at 4.80 m/s. What are the x-component and y-component of the velocity of the cruise ship relative to the patrol boat? (Assume that the +x-axis is east and the +y-axis is north. Enter your answers in m/s.)

Explanation:

We shall represent the velocity of cruise ship and coast guard petrol boat in vector form .

velocity of cruise ship

Vcs = - 2.5 j

Vpb =  - 4.8 cos 19 i + 4.8 sin 19 j = - 4.54 i + 1.56 j

velocity of the cruise ship relative to the patrol boat

= Vcs - Vpb

=  - 2.5 j - ( - 4.54 i + 1.56 j  )

=  - 2.5 j  +  4.54 i -   1.56 j  

= 2.04 i - 1.56 j .

x-component of the velocity of the cruise ship relative to the patrol boat

= 2.04 m /s

y-component of the velocity of the cruise ship relative to the patrol boat

= - 1.56 m /s .

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