I came across a question which I have been struggling to get the same answer as provided in the textbook: A parent holds a small child in a swing so that the angle of the swing support is at 20 degrees to the vertical. The child's weight is 200N and the swing seat weighs 50N. What horizontal force must the parent apply?
I started working through this by drawing a free-body diagram. From what I understand, the weight of the swing and the child is balanced by the vertical component of the tension in the swing support, so the vertical component of the tension in the swing support is 250N. The horizontal force that the parent must apply must be equal to the horizontal component of the tension in the swing support and so it equals 250tan20, which is 91N to 2 significant figures.
However, the answer provided in the textbook is 72.8N. I suspect that my diagram might not be entirely accurate. Have I somehow missed out some other forces? Is any of the forces in the diagram positioned incorrectly?
Thank you so much in advance.