Question

A 1100-kg car pulls a boat on a trailer. (a) what total force resists the motion of the car, boat, and trailer, if the car exerts a 1900-n force on the road and produces an acceleration of 0.550 m/s2 ? the mass of the boat plus trailer is 700 kg. (b) what is the force in the hitch between the car and the trailer if 80% of the resisting forces are experienced by the boat and trailer?

Answer 1

Refer to the diagram shown below.

R = total resistive force.
      80% of this force is experienced by the boat and trailer.
T =  the force in the hitch between the car and the trailer.

Overall motion:
Total mass = 1100 + 700 = 1800 kg
Acceleration = 0.55 m/s²
Driving force = 1900 N
Resisting force = R N
Therefore
(1900 - R N) = (1800 kg)*(0.55 m/s²)
1900 - R = 990
R = 910 N
0.2R = 182 N
0.8R = 728 N

Consider the motion of the car:
Driving force = 1900 N
Resistive force = 0.2R = 182 N
Force in the hitch  = T NAcceleration = 0.55 m/s²
Mass  = 1100 kg
Therefore
1900 - 0.2R - T = 1100*0.55
1900 - 182 -T = 605
T = 1113 N

Answer:
R = 910 N, the total resistive force.
T = 1113 N, the force in the hitch between the car and trailer.