Edit to “Solution”
en/1.1.1.md
+0 −30
| ### Statement | |||
| $1.1.1.$ Figure$^{*)}$ shows a "blurred photograph" of a jet airplane in flight. The length of the airplane is $30 \text{ m}$, the length of its nose is $10 \text{ m}$. Determine from this "photograph" the speed of the airplane. The shutter exposure time is $0.1 \text{ s}$. The shape of the airplane is shown in the figure with a dashed line. | |||
|  | |||
| #### Solution | |||
|  | |||
| To find the velocity of the airplane it is necessary to determine the vector of its displacement for the time $T$, during which the shutter of the camera is open. Let us select the initial point $1$ in the photograph and determine the distance it will move during the time $T$. The length of the airplane must be subtracted from the total length of the photograph. Taking into account the scale, the modulus of displacement will be | |||
| $$ | |||
| l=50-30 = 20 \text{ m} | |||
| $$ | |||
| For the $0.1 \text{ s}$ aiplane covered a distance of $20\text{ m}$, which corresponds to velocity of | |||
| @@ -18,33 +18,3 @@Solution | |||
| $$ | |||
| \boxed{v = \frac{l}{T} = 200\text{ m/s}} | |||
| $$ | |||
| − | |||
| − | #### O'zbekcha | ||
| − | |||
| − | $1.1.1.$ Rasmda*) uchayotgan reaktiv samolyotning | ||
| − | harakatdan ”siljigan” rasmi keltirilgan. Samolyot uzunligi $30 \text{ m}$ | ||
| − | burun qismining uzunligi $10 \text{ m}$. Mazkur ”siljigan” rasmga | ||
| − | ko’ra samolyot tezligini aniqlang ($m/s$). Rasmga olishda fotoapparat ekspozitsiya vaqti $0.1 \text{ s}$. Samolyot shakli rasmda | ||
| − | shtrixlab ko’rsatilgan | ||
| − |  | ||
| − | |||
| − | #### Yechim | ||
| − | |||
| − |  | ||
| − | Samolyotning tezligini aniqlash uchun kamera yopqichi ochiq bo‘lgan $T$ vaqt davomida uning siljish vektorini aniqlash zarur. Fotosuratda boshlang‘ich $1$ - nuqtani tanlaymiz va ushbu nuqta $T$ vaqt ichida qancha masofaga siljishini aniqlaymiz. Fotosuratdagi umumiy uzunlikdan samolyotning uzunligini ayirish kerak. Masshtabni hisobga olgan holda, siljishning moduli quyidagicha bo‘ladi: | ||
| − | |||
| − | $$ | ||
| − | l=50-30 = 20 \text{ m} | ||
| − | $$ | ||
| − | |||
| − | $0.1 \text{ s}$ davomida samolyot $20\text{ m}$ masofani o'tadi, bu orqali tezlikni topsak: | ||
| − | |||
| − | $$ | ||
| − | \boxed{v = \frac{l}{T} = 200\text{ m/s}} | ||
| − | $$ | ||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| ### Statement | ### Statement | ||
| $1.1.1.$ Figure$^{*)}$ shows a "blurred photograph" of a jet airplane in flight. The length of the airplane is $30 \text{ m}$, the length of its nose is $10 \text{ m}$. Determine from this "photograph" the speed of the airplane. The shutter exposure time is $0.1 \text{ s}$. The shape of the airplane is shown in the figure with a dashed line. | $1.1.1.$ Figure$^{*)}$ shows a "blurred photograph" of a jet airplane in flight. The length of the airplane is $30 \text{ m}$, the length of its nose is $10 \text{ m}$. Determine from this "photograph" the speed of the airplane. The shutter exposure time is $0.1 \text{ s}$. The shape of the airplane is shown in the figure with a dashed line. | ||
|  |  | ||
| #### Solution | #### Solution | ||
|  |  | ||
| To find the velocity of the airplane it is necessary to determine the vector of its displacement for the time $T$, during which the shutter of the camera is open. Let us select the initial point $1$ in the photograph and determine the distance it will move during the time $T$. The length of the airplane must be subtracted from the total length of the photograph. Taking into account the scale, the modulus of displacement will be | To find the velocity of the airplane it is necessary to determine the vector of its displacement for the time $T$, during which the shutter of the camera is open. Let us select the initial point $1$ in the photograph and determine the distance it will move during the time $T$. The length of the airplane must be subtracted from the total length of the photograph. Taking into account the scale, the modulus of displacement will be | ||
| $$ | $$ | ||
| l=50-30 = 20 \text{ m} | l=50-30 = 20 \text{ m} | ||
| $$ | $$ | ||
| For the $0.1 \text{ s}$ aiplane covered a distance of $20\text{ m}$, which corresponds to velocity of | For the $0.1 \text{ s}$ aiplane covered a distance of $20\text{ m}$, which corresponds to velocity of | ||
| @@ -18,33 +18,3 @@Solution | |||
| $$ | $$ | ||
| \boxed{v = \frac{l}{T} = 200\text{ m/s}} | \boxed{v = \frac{l}{T} = 200\text{ m/s}} | ||
| $$ | $$ | ||
| #### O'zbekcha | |||
| $1.1.1.$ Rasmda*) uchayotgan reaktiv samolyotning | |||
| harakatdan ”siljigan” rasmi keltirilgan. Samolyot uzunligi $30 \text{ m}$ | |||
| burun qismining uzunligi $10 \text{ m}$. Mazkur ”siljigan” rasmga | |||
| ko’ra samolyot tezligini aniqlang ($m/s$). Rasmga olishda fotoapparat ekspozitsiya vaqti $0.1 \text{ s}$. Samolyot shakli rasmda | |||
| shtrixlab ko’rsatilgan | |||
|  | |||
| #### Yechim | |||
|  | |||
| Samolyotning tezligini aniqlash uchun kamera yopqichi ochiq bo‘lgan $T$ vaqt davomida uning siljish vektorini aniqlash zarur. Fotosuratda boshlang‘ich $1$ - nuqtani tanlaymiz va ushbu nuqta $T$ vaqt ichida qancha masofaga siljishini aniqlaymiz. Fotosuratdagi umumiy uzunlikdan samolyotning uzunligini ayirish kerak. Masshtabni hisobga olgan holda, siljishning moduli quyidagicha bo‘ladi: | |||
| $$ | |||
| l=50-30 = 20 \text{ m} | |||
| $$ | |||
| $0.1 \text{ s}$ davomida samolyot $20\text{ m}$ masofani o'tadi, bu orqali tezlikni topsak: | |||
| $$ | |||
| \boxed{v = \frac{l}{T} = 200\text{ m/s}} | |||
| $$ | |||