Final answer:
The resultant force exerted by the two cables on the traffic light is found through a free-body diagram, with the vertical components of tension balancing the weight of the traffic light and horizontal components canceling each other out.
Step-by-step explanation:
To find the resultant force exerted by the two cables supporting the traffic light, we'll need to consider the system's free-body diagram as provided in the figures mentioned. Each tension force in the cables has both vertical and horizontal components due to the angles at which the cables are positioned.
According to the figures and information given, we use the strategy that involves projecting the forces onto a coordinate system with a vertical axis (y-axis) and a horizontal axis (x-axis). For equilibrium, the sum of the vertical components needs to be equal to the weight of the traffic light, and the horizontal components must cancel out.
The weight of the traffic light can be calculated as the mass (15.0 kg) times the acceleration due to gravity. With this weight and the angles provided by the cables, we can use trigonometry to find the vertical component of each cable's tension. Then, using the requirement that the horizontal components cancel out, we can find the tension in each wire.