Fred, Betsy and Joe all pull a tire. The tire's mass is M = 75 kg. The force of each person is

Fred: F_fred to the East
Betsy: 340 N to the North
Joe: 400 N at an angle theta South of West

The net result is that the tire accelerates slowly to the North, at a = 1.0 m/s².

What is the angle theta?

How hard is Fred pulling?

   force        x            y
  --------------------------------
           |          |         
           |          |         
           |          |         
           |          |         
           |          |         
           |          |         
           |          |         
           |          |         
  --------------------------------
   total   |          |
  --------------------------------



                x           y
  --------------------------------
   accel   |          |
           |          |
  --------------------------------

If you have time ...

The kids take a break, then start pulling again. This time, things are a little different:

Betsy still pulls North at 340 N
Fred still pulls East, but with a force of 250 N
Joe pulls with a new force F_Joe at a different angle theta
the tire does accelerate North at 1 m/s^2 again

Can you figure out the magnitude and direction of F_Joe?