Wind foils the plan

A ballistic missile is projected from ground with speed \(100m/s\) making \(37° \) with horizontal. After 8 seconds of projection a strong wind starts blowing in the direction of motion imparting an acceleration of \(25m/{ s }^{ 2 }\). The missile which was to land in enemy's camp is now heading to ally's camp. Find \(\left[ minimum\quad projection\quad speed \right] \) of the anti-ballistic missile to destroy the ballistic missile if it takes 1 second to deploy it. Assume acceleration imparted by wind to both ballistic missile and anti-ballistic missile is same.

\(g=10m/{s}^{2} \)

\(\cos { 37° } =\frac { 4 }{ 5 } \)

This problem is originally part of set Mechanics problems by Abhishek Sharma.

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