question_answer

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

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

B)  10 \[\sqrt{31}m{{s}^{-1}}\]

C)  \[50\text{ }m{{s}^{-1}}\]

D)  \[30\text{ }m{{s}^{-1}}\]

Correct Answer: C

Solution :

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