An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < -6 N , 3 N># and the second is #F_2 = < 6 N, 5 N>#. What is the object's rate and direction of acceleration?
When you want to sum two vectors in classical mechanics, it is enough if you sum them component by component.
The final vector is
The length of a vector is given by
that of our vector is
Then the force is with a magnitude of 8N and the acceleration is given by
The direction is given by
This of course is a problem because we cannot divide by zero. On the other hand we know that the arctan is singular when the angle is