You are a soldier, and your base is under attack by enemy aircraft. At time t=0, one such aircraft is positioned at (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).
Also at 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, and it can be aimed in any direction. Your position is (x,y,z)=(0 m, 0 m, 0 m).
There is an ambient gravitational acceleration of 10 m/s2 in the −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).