A tank fires a projectile at an angle of \(\si{60\ \deg}\) with the horizontal to destroy a target. Immediately the Commanding Officer realizes that they have fired at one of their own outposts and orders the crew to fire another projectile at an angle of \(\si{45\ \deg}\) after some time to destroy the earlier projectile in mid air. After how much time (in seconds) was the second projectile fired?

**Details and Assumptions**

- Muzzle velocity of both the projectiles is \(\si{1670\ \meter/\second}\) .
- \(g=\si{10\ \meter/\second^2}\)
- Report your answer to 3 decimal places.

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