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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