# A shell is projected from a level ground with a velocity of $20\;m/s$ at $45^{\circ}$ to the horizontal. When the shell is at highest point, it breaks into two equal fragments. One of the fragment whose initial velocity after the explosion is zero, falls vertically downward. At what distance from the point of projection does the other fragment fall? $(g=10\;ms^{-2})$

$\begin {array} {1 1} (a)\;30\;m & \quad (b)\;60\;m \\ (c)\;90\;m & \quad (d)\;40\;m \end {array}$

Since centre of mass motion will not be affected by the explosion, it will be at a distance $R$ =range from the point of projection .
=> Total distance of the 2 nd mass from the point of projection is $\large\frac{3R}{2}$
$S= \large\frac{3}{2} \times \frac{u^2}{2g}$
$\quad= \large\frac{3}{2} \times \frac{20 \times 20}{20}$
$\quad= 30 \;m$
answered Nov 21, 2013 by
edited Jun 17, 2014