In the overhead view of cookie tin is accelerated in the direction shown by a, over a friction less horizontal surface.

SOLUTION: One Key Idea here is that the pet force on the tin is the sum of the three forces and is related to the acceleration a of the tin via Newton’s law Thus,

A second Key Idea is that this is a two-dimensional problem; so we cannot find merely by substituting the magnitudes for the vector quantities on the right side . We must vector the reverse the reverse as is shown.

Then, substituting known data, we find

Similarly, along the y axis we find

We can now use a vector-capable calculator to get the magnitude and the angle .We can also use obtain the magnitude and the angle (from the positive direction of the x axis) as