Question about Vectors and how the change in direction from the wind affects it.

[McWilliams]

(The National Hockey League has closed its doors. This is the best we can do for sport.)

I suggest that you make East the x-axis and North the y-axis. Neither axis is up or down, both are along the ground.

Allan is skating East on a flat ice rink at 4.0 m/s. The wind is blowing constantly towards North East (at 45 degrees between North and East) and accelerates Allan in the same direction with a magnitude of 1.0 m/s2. If Allan starts at the origin at time t1=0, where will he be at t2, 10. seconds later?

I am looking for a little guidance on this question, i have attempted it a few times but as of yet, I don't even know if i am on the right track, If someone could just send me on the right track i would greatly appreciated it.

I had made the diagram of how the wind had affected the original path of Allan, and i believe i need to calculate a final velocity before i can use time to determine his position, I tried to do it through for the x direction vicos(45) which came out to be 2.83m/s then i added 4.0m/s to get a total of 6.83m/s and a total distance of 68.3m in the x direction. Although i do not believe this is right.

 

[jbsteele]

To answer this question, you should use the equation of motion, which states that the change in velocity (Δv) is equal to the acceleration (a) multiplied by the time (t). In this case, the acceleration is 1.0 m/s2, and the time is 10 seconds. This means that the change in velocity is 10 m/s. The initial velocity was 4.0 m/s, so the final velocity is 14.0 m/s, with a component of 6.83 m/s in the East direction and 7.07 m/s in the North East direction. Using this final velocity, you can then calculate the displacement in both the East and North East directions by multiplying the velocity by the time again. The displacement for the East direction would be 68.3 m and for the North East direction it would be 70.7 m. Adding these two displacements together gives you the total displacement from the origin, which would be 139 m.