I need to rank cars by the largest speed considering the acting forces on these cars: #1 has 5N applied in forward direction and 10N against the direction at 45 deg. #2 has no force applied in forward direction but 10N applied at 90 deg. Which car has a larger speed???

Question

anonymous · Answer

here is picture of the car ranking problem

carson889 · Answer

You are trying to determine which car has the highest NET force being applied to it. You want to calculate the sum of the forces forward and backward, and determine which one is the highest.

ie:

The top left picture has a forward force of 5N. The backwards force is two seperate 5N forces at 45 degree angles to the car. Thus, we want to find the horizontal/x-axis force against the car. So we multiply the force by cos(45) and get 3.5355N. Since there is two of those forces the total backwards force equals 7.071N. The net force on the car is thus: 
Force forwards - force backwards = 10N - 7.071N = 2.929 N [forwards]. 

It would also be possible to rank them with intuition ie: recognizing the 10N forward force will have a greater net force than the 5N force with the same backwards force being applied to it. Top left and top middle pictures.  Also there are three cars with zero net force being applied.

anonymous · Answer

how would I calculate the force for the middle top car that has no force forward but two 5N forces from the side at 90 deg. 0 N * sin 90, so the two side forces have no effect ???