question_answer

A projectile is moving at \[20\,\text{m}{{\text{s}}^{-1}}\]at its highest point, where it breaks into equal parts due to an internal explosion. One part moves vertically up at \[30\,\text{m}{{\text{s}}^{-1}}\]with respect to the ground. Then the other part will move at:

A) \[20\,m{{s}^{-1}}\]                         

B) \[10\sqrt{31}\,m{{s}^{-1}}\]

C)  \[50\,m{{s}^{-1}}\]                        

D)  \[30\,m{{s}^{-1}}\]

Correct Answer: C

Solution :

\[{{p}_{i}}m\,u\] \[=\,m\,20\] \[\therefore \]  \[|{{p}_{i}}|\,=\,|{{p}_{2}}+{{p}_{3}}|\] \[{{p}_{3}}=\sqrt{p_{i}^{2}+{{({{p}_{2}})}^{2}}}\] \[\frac{m\upsilon }{2}=\sqrt{{{m}^{2}}{{(20)}^{2}}+{{\left( \frac{m}{2}30 \right)}^{2}}}\] \[\frac{m\upsilon }{2}=\frac{m}{2}\sqrt{{{(40)}^{2}}+{{(30)}^{2}}}\] \[\upsilon =50\,m/\sec \]