Question

Viteza unui avion de vinatoare e egala cu 200 m/s. din avion se impusca cu un pistol in sensul zborului avionului si in sensul opus lui.de cite ori difera energiile cinetice ale gloantelor ,daca vitezele lor fata de pistol sint 600 m/s.

Answer 1

Notatii: $\vec{v_a}$ – viteza absoluta, $\vec{v_r}$ – viteza relativa, $\vec{v_t}$ – viteza de transport (a avionului)

$\vec{v_{a1}}=\vec{v_{r1}}+\vec{v_t}\implies v_{a1}=v_{r1}+v_{t}$

$\vec{v_{a2}}=\vec{v_{r2}}+\vec{v_t}\implies v_{a2}=v_{r2}-v_{t}$

$E_{c1}=\frac{1}{2}mv_{a1}^2, E_{c2}=\frac{1}{2}mv_{a2}^2\implies \frac{E_{c1}}{E_{c2}}=\left(\frac{v_{a1}}{v_{a2}}\right)^2$

$\dfrac{E_{c1}}{E_{c2}}=\left(\dfrac{v_r+v_t}{v_r-v_t}\right)^2$

Numeric, $\dfrac{E_{c1}}{E_{c2}}=\left(\dfrac{800}{400}\right)^2=4$