question_answer

A shell is fired from a cannon with a velocity u at an angle \[\theta \] with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal mass. One of the pieces retraces its path of the cannon. Speed of the other piece immediately after the explosion is

A)  \[3\,v\,\cos \,\theta \]  

B)         \[2\,v\,\cos \,\theta \]

C)  \[\frac{3}{2}\,v\,\cos \,\theta \]              

D)         \[\frac{\sqrt{3}}{2}\,v\,\cos \,\theta \]

Correct Answer: A

Solution :

We know, Initial momentum \[=\] Final momentum \[\therefore \]    \[mv\cos \theta =\frac{m}{2}\times {{v}_{1}}-\frac{m}{2}\times v\cos \theta \] \[\Rightarrow \]   \[2v\cos \theta ={{v}_{1}}-\cos \theta \] \[\Rightarrow \]   \[{{v}_{1}}=3v\cos \theta \]