Đáp án:
$\begin{align}
& a)P=12,5kg.m/s \\
& b)P=3,5kg.m/s \\
& c)P=9,2kg.m/s \\
& d)P=11kg.m/s \\
\end{align}$
Giải thích các bước giải:
động lượng mỗi vật:
$\begin{align}
& {{P}_{1}}={{m}_{1}}.{{v}_{1}}=1,5.3=4,5kg.m/s \\
& {{P}_{2}}={{m}_{2}}.{{v}_{2}}=4.2=8kg.m/s \\
\end{align}$
Bảo toàn động lượng:
$\overrightarrow{P}=\overrightarrow{{{P}_{1}}}+\overrightarrow{{{P}_{2}}}$
a) $\overrightarrow{{{v}_{1}}}\uparrow \uparrow \overrightarrow{{{v}_{2}}}\Rightarrow \overrightarrow{{{P}_{1}}}\uparrow \uparrow \overrightarrow{{{P}_{2}}}$
Ta có: $P={{P}_{1}}+{{P}_{2}}=4,5+8=12,5kg.m/s$
b)
$\overrightarrow{{{v}_{1}}}\uparrow \downarrow \overrightarrow{{{v}_{2}}}\Rightarrow \overrightarrow{{{P}_{1}}}\uparrow \downarrow \overrightarrow{{{P}_{2}}}$
ta có:
$P=\left| {{P}_{1}}-{{P}_{2}} \right|=\left| 4,5-8 \right|=3,5kg.m/s$
c) $\overrightarrow{{{v}_{1}}}\bot \overrightarrow{{{v}_{2}}}\Rightarrow \overrightarrow{{{P}_{1}}}\bot \overrightarrow{{{P}_{2}}}$
ta có: $P=\sqrt{P_{1}^{2}+P_{2}^{2}}=\sqrt{4,{{5}^{2}}+{{8}^{2}}}=9,2m/s$
d) $\widehat{\left( \overrightarrow{{{v}_{1}}};\overrightarrow{{{v}_{2}}} \right)}={{60}^{0}}\Rightarrow \widehat{\left( \overrightarrow{{{P}_{1}}};\overrightarrow{{{P}_{2}}} \right)}={{60}^{0}}$
ta có:
$\begin{align}
& P=\sqrt{P_{1}^{2}+P_{2}^{2}+2.{{P}_{1}}.{{P}_{2}}.c\text{os}\alpha } \\
& =\sqrt{4,{{5}^{2}}+{{8}^{2}}+2.4,5.8.cos60} \\
& =11kg.m/s \\
\end{align}$
