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? $(g=10\;ms^{-2})$

Question

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