Question

Para um observador, dois objetos A e B, de massas iguais, movem-se com velocidades constantes de 20 km/h e 30 km/h, respectivamente. Para o mesmo observador, qual é a razão \(\frac{E_CA}{E_CB}\) entre as energias cinéticas desses objetos?

Answer 1

$\Large\boxed{\begin{array}{l}\sf E_C(A)=\dfrac{1}{2}\cdot m\cdot v^2\\\\\sf E_C(A)=\dfrac{1}{2}\cdot m\cdot20^2\\\\\sf E_C(A)=\dfrac{400\cdot m}{2}\\\\\sf E_C(A)=200\cdot m\end{array}}$

$\Large\boxed{\begin{array}{l}\sf E_C(B)=\dfrac{1}{2}\cdot m\cdot v^2\\\\\sf E_C(B)=\dfrac{1}{2}\cdot m\cdot 30^2\\\\\sf E_C(B)=\dfrac{900\cdot m}{2}\\\\\sf E_C(B)=450\cdot m\end{array}}$

$\Large\boxed{\begin{array}{l}\bf Raz\tilde a o:\\\sf \dfrac{E_C(A)}{E_C(B)}=\dfrac{200\cdot\not m}{450\cdot\not m}\\\\\sf \dfrac{E_C(A)}{E_C(B)}=\dfrac{200^{\div50}}{450_{\div50}}\\\\\sf \dfrac{E_C(A)}{E_C(B)}=\dfrac{4}{9}~\checkmark\end{array}}$