[latex]alpha = 15\ eta = ?\ z_1 = frac{v_o^2cdot sin2alpha}{g}\ z_2 = 2cdot z_1\ [/latex] [latex]frac{v_0cdot sin2eta}{g}=2cdot frac{v_0cdot sin2alpha}{g} /:v_0^2cdot g\ sin2eta=2sin2alpha\ sin2eta = 2cdot sin30\ sin2eta = 2cdot frac{1}{2}\ sin2eta=1\ 2sineta coseta = 1 /:2\ sineta coseta = frac{1}{2} /^2\ sin^2eta cos^2eta = frac{1}{4} cos^2eta =1-sin^2eta\ sin^2eta (1-sin^2eta) = frac{1}{4}\ sin^2eta - sin^4eta -frac{1}{4}=0 /cdot (-1)\ sin^4eta -sin^2eta +frac{1}{4}=0\ (sin^2eta - frac{1}{2})^2=0\ [/latex] [latex]sin^2eta -frac{1}{2}=0\ sin^2eta = frac{1}{2}\ sineta = sqrt{frac{1}{2}}\ sineta = frac{sqrt{2}}{2}\ eta = 45^o[/latex]
[latex]dane:\alpha = 15^{o}\X_1 = frac{v_{0}^{2}sin2alpha}{g}\X_2 = 2X_1\szukane:\eta = ?[/latex] [latex]frac{v_{0}^{2}sin2eta}{g} =2cdot frac{v_{0}^{2}sin2alpha}{g} |cdotfrac{g}{v_{0}^{2}}\\sin2eta = 2sin2alpha\\sin2alpha = sin(2cdot15^{o}) = sin30^{o} = frac{1}{2}\\sin2eta = 2cdotfrac{1}{2}\\sin2eta = 1\\2eta = 90^{o} /:2\\eta = 45^{o}[/latex] Odp. Ciało należy rzucić pod kątem 45° do poziomu.
