គណនាវិនាទីបាញ់យន្តហោះ

Question Statement:-

An enemy jet is flying at a constant height of 250 m250 m with a velocity of 500 m/s500 m/s. The fighter jet passes over an anti-aircraft gun that can fire at any time and in any direction with a speed of 100 m/s100 m/s. Determine the time interval during which the fighter jet is in danger of being hit by the gun bullets.

Source:- Mechanincs for JEE (Main & Advanced) (Vol.-1) - Er. Anurag Mishra

សំនួរក្នុងស្ថានភាព
យន្តហោះខ្មាំងហោះក្នុងកំពស់ថេរគឺ ២៥០ម ក្នុងល្បឿន ៥០០ម/វិនាទី។ យន្តហោះប្រយុទ្ធខ្មាំងហោះពីលើមូលដ្ឋានកាំភ្លើងធំការពារអាកាសរបស់យើង ដែលអាចនឹងធ្វើការវាយប្រហារមកយើងគ្រប់ពេល និងពីគ្រប់ទិស ក្នុងល្បឿន ១០០ម/វិនាទី។ ចូរកំណត់ថាតើកាំភ្លើងការពារអាកាសគួរបាញ់ពេលណាឲ្យបានមុខខ្មាំងបាញ់យើង?៕


Anti-Aircraft Marksman
Classical Mechanics Level 3
You are a soldier, and your base is under attack by enemy aircraft. At time t=0t=0, one such aircraft is positioned at (x,y,z)=(1000 m, 2000 m, 3000 m).(x,y,z)=(1000 m, 2000 m, 3000 m). The aircraft has a constant velocity of (vx,vy,vz)=(−400 m/s, +400 m/s, +400 m/s).(vx,vy,vz)=(−400 m/s, +400 m/s, +400 m/s).
Also at t=0,t=0, you take control of an anti-aircraft artillery cannon and fire a shot to bring down the enemy plane. The cannon has a muzzle velocity of 1000 m/s,1000 m/s, and it can be aimed in any direction. Your position is (x,y,z)=(0 m, 0 m, 0 m).(x,y,z)=(0 m, 0 m, 0 m).

There is an ambient gravitational acceleration of 10 m/s210 m/s2 in the −z−z direction (downward).
At what time (in seconds) does the artillery shell strike the enemy plane?


Details and Assumptions:

Neglect air resistance.
Give your answer to 2 decimal places.
From a targeting perspective, consider the enemy plane to be a point-particle.
You are a superlative marksman.
If you find more than one solution, give the smaller value (provided that it's not negative).