Math  /  Geometry

Question1. Two teenagers are pulling on ropes attached to a tree. The angle between the ropes is 30.030.0^{\circ}. David pulls with a force of 400.0 N and Stephanie pulls with a force of 300.0 N . (a) Find the component form of the net force. (b) Find the magnitude of the resultant (net) force on the tree and the angle it makes with David's rope.

Studdy Solution
Calculate the angle θ\theta: θ=tan1(150.0N659.8N) \theta = \tan^{-1}\left(\frac{150.0 \, \text{N}}{659.8 \, \text{N}}\right) θtan1(0.2273) \theta \approx \tan^{-1}(0.2273) θ12.8 \theta \approx 12.8^\circ
The component form of the net force is (659.8N,150.0N) (659.8 \, \text{N}, 150.0 \, \text{N}) . The magnitude of the resultant force is approximately 676.6N 676.6 \, \text{N} , and the angle it makes with David's rope is approximately 12.8 12.8^\circ .

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