A child weighing 150 newtons is sitting in a swing. the swing is supported by two ropes, one on each side. what is the tension in one of the ropes?

The tension in the ropes depends on the angle of the ropes with the vertical, but in any case, the sum of all forces must be zero. If the force on the swing is 150N downwards, then the two ropes must pull upwards with the same force. Each rope has to pull upwards with 75 N. All horizontal forces must cancel. The tension in the ropes consists of the sum of the vertical and horizontal forces.