Problem 7.41

จาก \(\vec{u}_{12}= \vec{u}_{1E}+ \vec{u}_{E2}\)

\(\vec{u}_{12}= \vec{u}_{1E}- \vec{u}_{2E}\)

îĵî

\(\vec{u}_{12}= (ucos\theta + usin\theta ) - (-v )\)

îĵ

\(\vec{u}_{12}= (ucos\theta + v) + usin\theta\)

จาก \(\vec{a}_{12}= \vec{a}_{1E}+ \vec{a}_{E2}\)

ĵĵ

\(\vec{a}_{12}= \vec{a}_{1E}- \vec{a}_{2E}= (-g ) - (0) = -g\)

จาก\(\vec{s}_{12}=\vec{u}_{12}t+\frac{1}{2}\vec{a}_{12}t^{2}\)

îĵîĵĵ

\(\ell +0=((ucos\theta +v)+usin\theta )t+\frac{1}{2}(-g)t^{2}\)

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

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

และ \(\ell = (ucosθ + v)t\)

\(\ell = (ucos\theta + v)(\frac{2usin\theta}{g})\)

\(\therefore v =\frac{g\ell}{2usin\theta}- ucos\theta =\frac{g\ell  - u^{2}\sin 2\theta}{2usin\theta}\;\blacksquare\)