Problem 13.39

จาก \(Σ\vec{F} = m\vec{a}\) และ\(K=\frac{1}{2}mv^{2}\)

ĵ

\(-qE = m\vec{a}v = \pm \sqrt{\frac{2K}{m}}\)

ĵ

\(\vec{a} = -\frac{qE}{m}\therefore v =\sqrt{\frac{2K}{m}}\)

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

îĵîĵĵ

\(x + 0 = (\sqrt{\frac{2K}{m}}\cos \theta +\sqrt{\frac{2K}{m}}\sin \theta )t+\frac{1}{2}(-\frac{qE}{m})t^{2}\)

îĵîĵ

\(x + 0 =\sqrt{\frac{2K}{m}}tcos\theta + (\sqrt{\frac{2K}{m}}tsin\theta -\frac{qEt^{2}}{2m})\)

\(\therefore 0 =\sqrt{\frac{2K}{m}}tsin\theta -\frac{qEt^{2}}{2m}\)

\(t = 0,\frac{2msin\theta}{qE}\sqrt{\frac{2K}{m}}\)

\(\therefore t =\frac{2msin\theta}{qE}\sqrt{\frac{2K}{m}}\)

และ \(x = \sqrt{\frac{2K}{m}}tcos\theta\)

\(x =\sqrt{\frac{2K}{m}(}\frac{2msin\theta}{qE}\sqrt{\frac{2K}{m}})\cos \theta =\frac{4Ksin\theta \cos \theta}{qE}\;\blacksquare\)