Question

Un corp cade liber de la inaltimea de 60m care e viteza corpului la sfarsitul caderii? ..care e timpul total de cadere a acestui corp pana la sol?...pentru carpul mentionat calculati care era inaltimea arcursa la jumatea timpului de cadere?

Answer 1

   
[tex]\displaystyle\\ \texttt{Un corp cade liber de la inaltimea de 60m.}\\\\ a)~~\texttt{Care e viteza corpului la sfarsitul caderii?}\\ \text{Folosim Formula lui \bf Galileo Galiliei:} \\ v^2=v_0^2+2a(x-x_0)\\ unde\!\!: ~v_0 = 0; ~a = g \approx 10;~ (x-x_0) = h = 60~m;\\ v = \text{viteza la sfarsitul caderii} \\\\ v^2 = 2gh \\ v= \sqrt{2gh} =\sqrt{2\times 10 \times 60} =\sqrt{1200} =\boxed{\bf20 \sqrt{3}~m\!/\!s} \approx \boxed{34,\!6~m\!/\!s} [/tex]


[tex]\displaystyle\\ b)\\ \texttt{Care e timpul total de cadere a acestui corp pana la sol?}\\ \text{Folosim formula: }\\ x=x_0+v_0t+ \frac{at^2}{2} \\ \text{unde: }\\x = h=60~m;~x_0=0;~v_0 = 0; ~a = g \approx 10; \\t=\text{timpul total de cadere pana la sol.}\\\\ h = \frac{gt^2}{2}\\\\ gt^2 = 2h\\\\ t^2 = \frac{2h}{g} \\\\ t = \sqrt{\frac{2h}{g}}= \sqrt{\frac{2\times60}{10}}=\sqrt{\frac{120}{10}}= \sqrt{12} = \boxed{\bf 2\sqrt{3}~s} \approx \boxed{\bf 3,\!46~s}\\\\\\ [/tex]


[tex]\displaystyle\\ c)\\ \texttt{Pentru carpul mentionat calculati care era inaltimea }\\ \texttt{parcursa la jumatea timpului de cadere?} \\ \text{Folosim formula: }\\ x=x_0+v_0t_m+ \frac{at_m^2}{2} \\ \text{unde: }\\ x = \text{distanta parcursa in cadese de la h = 60 m }\\ \text{pana la jumatatea timpului de cadere};\\ x_0=0;~v_0 = 0; ~a = g \approx 10; \\ t_m = \frac{t}{2}= \frac{2 \sqrt{3} }{2} = \sqrt{3}~s =\text{jumatate din timpul total de cadere pana jos.} [/tex]

[tex]\displaystyle\\ x = \frac{gt_m^2}{2}= \frac{10\times \Big( \sqrt{3} \Big)^2}{2}= \frac{10\times 3}{2}=\frac{30}{2}=\boxed{15~m }\\\\ \texttt{x = 15 m este distanta parcursa de la inaltimea de 60 m }\\ \texttt{pana cand a trecut jumatate din timpul de cadere la sol.}\\\\ h_m = 60 - x = 60 - 15 = \boxed{\bf 45~m}\\\\ \texttt{Inaltimea }h_m} \texttt{ este inaltimea fata de sol la care se afla}\\ \texttt{ cand a trecut jumatate din timpul de cadere.} [/tex]