Rank Velocity Vectors by Kinetic Energy

[vysero]

Rank the following velocities according to the kinetic energy a particle will have with each velocity, greatest first: (a) v = 4i +3j, (b) v = -4i +3j, (c) v = -3i + 4j, (d) v = 3i - 4j, (e) v = 5i, and (f) v = 5 m/s at 30 degrees to the horizontal.



K = 1/2mv^2



I am not sure how to start.

I am sure this question is rather easy considering it is the very first question after the chapter. However, I read the chapter 2x and they never mention finding kinetic energy given velocity vectors... Maybe someone could explain to me how I should start this problem or what the key ideas here are. When I see velocity vectors I see points on a graph, maybe I should be looking at them differently?

 

[voko]

Velocity is a vector, so it has a direction and it has a magnitude. The latter is commonly known as speed. Kinetic energy is proportional to the square of magnitude.