Question

Vă rog urgent!!! Dau coroană

Answer 1

[tex]\displaystyle \text{Se da:}\\ \\ \alpha=30^\circ\\ \\ t_1=3s\\ \\ t_2=5s\\ \\ h_1=h_2=h\\ \\ g=10\frac m{s^2}\\ \\ v_0=?\frac ms\\ \\ h=?m\\ \\ \\[/tex]


[tex]\displaystyle \text{Formule:}\\ \\ h_1\text{ si } h_2 \text{ reprezinta inaltimi, deci lucram cu axa O}_\text {y}\\ \\ \\ \text{Ecuatia de miscare a obiectului pe axa O}_\text{y}:\\ \\ h(t)=v_{0_y}\times t-\frac {g\times t^2}2\\ \\ \\ \text{Unde }v_{0_y} \text{reprezinta viteza initiala pe axa O}_\text{y}:\\ \\ \\ v_{0_y}=v_0\times\sin\alpha,\text { prin urmare:}\\ \\ \\[/tex]


[tex]\displaystyle h(t)=v_0\times\sin\alpha\times t-\frac{g\times t^2}{2}\\ \\ \\ \text{Folosind formula pentru momentul }t_1\text{ si }t_2:\\ \\ \\ 1)h_1=v_0\times\sin\alpha\times t_1-\frac{g\times t_1^2}{2}\\ \\ 2)h_2=v_0\times\sin\alpha\times t_2-\frac{g\times t_2^2}{2}\\ \\ \\ \text{Iar deoarece avem }h_1=h_2:\\ \\ \\ v_0\times\sin\alpha\times t_1-\frac{g\times t_1^2}{2}=v_0\times\sin\alpha\times t_2-\frac{g\times t_2^2}{2}\\ \\ \\ \text{De unde usor scoatem }v_0:\\ \\ \\[/tex]


[tex]\displaystyle v_0\times\sin\alpha\times t_1-v_0\times\sin\alpha\times t_2=\frac{g\times t_1^2}{2}-\frac{g\times t_2^2}{2}\\ \\ v_0\times\sin\alpha\times(t_1-t_2)=\frac g2\times(t_1^2-t_2^2)\\ \\ v_0\times\sin\alpha\times(t_1-t_2)=\frac g2\times(t_1-t_2)\times(t_1+t_2)\\ \\ v_0\times\sin\alpha=\frac g2\times (t_1+t_2)\\ \\ \\ \boxed{v_0=\frac{g\times(t_1+t_2)}{2\times\sin\alpha}}\\ \\ \\ \\ \text{Pentru }h\text{ inlocuim }v_0 \text{ intr-o ecuatie, de ex. in prima}:\\ \\ \\[/tex]


[tex]\displaystyle h=\frac{g\times(t_1+t_2)\times\sin\alpha\times t_1}{2\times\sin\alpha}-\frac{g\times t_1^2}{2}\\ \\ h=\frac{g\times t_1\times(t_1+t_2)}{2}-\frac{g\times t_1^2}2\\ \\ h=\frac {g\times[t_1\times(t_1+t_2)-t_1^2]}2\\ \\ h=\frac{g\times(t_1^2+t_1\times t_2-t_1^2)}{2}\\ \\ \\ \boxed{h=\frac{g\times t_1\times t_2}2}\\ \\ \\ \text{Calcule:}\\ \\ v_0=\frac{10\times(3+5)}{2\times\sin30}=80\frac ms\\ \\ h=\frac{10\times 3\times5}2=75m[/tex]