John and Mary are skating at an ice rink. John skates at a constant speed of 6.7 m/s, with respect to the ice surface, directly south. Mary skates at a constant speed of 11.5 m/s in a direction of 34° west of south, with respect to the ice. What are the magnitude and direction of Mary's velocity with respect to John? Give the direction as measured relative to due south.

I don't understand how to graph this question. SOMEONE PLEASE HELP.

1 answer

using vectors,
John's velocity is <0,-6.7>
Mary's velocity is <-6.43,-9.53>

Mary's velocity with respect to John is the difference between their velocities:

<-6.43,-9.53> - <0,-6.7> = <-6.43,-2.83>
Now just get the magnitude and direction of that vector:

7.03m/s at W23.7°S