A 1200 kg car pushes a 2100 kg truck that has a dead battery to the right. When the driver steps on the accelerator, the drive wheels of the car push against the ground with a force of 4500 N . What is the magnitude of the force the car applies to the truck?

Question

What is the magnitude F_ct of the force that the car exerts on the truck? where the positive y direction is upward, and the positive x direction is to the right, the direction in which F_ct_vec points.

Answer 1

The 4500 N force on the car's tires accelerates the car and the truck together at a rate
a = 4500/(1200+2100) = 1.364 m/s
(assuming the pushed truck offers no resistance).
The force applied to the truck is is
Mtruck*a = 2864 N

The second part of your question seems repetitive. I do not understand your notation.