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enter image description hereI 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.

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closed as off-topic by John Rennie, AccidentalFourierTransform, RedGrittyBrick, glS, user36790 Oct 28 '16 at 18:44

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    $\begingroup$ Hi and welcome to the Physics SE! Please note that this is not a homework help site. Please see this Meta post on asking homework questions and this Meta post for "check my work" problems. $\endgroup$ – John Rennie Oct 28 '16 at 14:39
  • $\begingroup$ What is your answer and what was your process of getting there? $\endgroup$ – Michael Oct 28 '16 at 16:03
  • $\begingroup$ Nice diagram, but isn't it missing the parent's holding force? That should be horizontally left-wards, no? $\endgroup$ – Steeven Oct 30 '16 at 13:01
  • $\begingroup$ Ah, yes, thank you. But surely, wouldn't that still give 91N as the answer for the horizontal force applied by the parent, not 72.8N as said by the textbook? $\endgroup$ – panginuk Oct 30 '16 at 14:38
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Draw a Free Body Diagram of the forces on the swing seat. The forces acting on it are : weight of child vertically down, tension in chain acting at 20 degrees to the vertical, and the pull from the parent, acting horizontally opposite side to the chain. These forces are balanced, so the totals of horizontal and vertical components must each be zero.

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