Problem 7.39

กำหนดให้แกน x เอียงตามแนวพื้นเอียง

จาก\(\vec{s}=\vec{u}t+\frac{1}{2}\vec{a}t^{2}\)

îĵîîîĵ

\(r+0=(ucos\theta +usin\theta )t+\frac{1}{2}(-gsinφ-gcosφ)t^{2}\)

îĵîĵ

\(r + 0 = (utcos\theta -\frac{gt^{2}\sin φ}{2}) + (utsin\theta -\frac{gt^{2}\cos φ}{2})\)

\(\therefore 0 = utsin\theta -\frac{gt^{2}\cos φ}{2}\)

จะได้ \(t = 0, \frac{2usin\theta}{gcosφ}\to \therefore t =\frac{2usin\theta}{gcosφ}\)

และ \(r = utcosθ - \frac{gt^{2}\sin φ}{2}\)

\(r = (ucos\theta )(\frac{2usin\theta}{gcosφ})+\frac{1}{2}(-gsinφ)(\frac{2usin\theta}{gcosφ})^{2}\)

\(r =\frac{2u^{2}\sin \theta (\cos \theta  - \sin \theta \tan φ)}{gcosφ}\;\blacksquare\)