Firework mortars work by firing a shell into the sky before having it explode in a shower of lights for everyone to enjoy. Due to the large explosions, they tend to be launched out over a lake or other body of water. For safety, the launch tubes are placed as close to the ground as they can manage.

A mortar works by containing a small initial explosion that accelerates a 250-gram shell from rest to a speed of 325 m/s in 0.1 seconds. In order to get height and forward motion, the launch tubes are set at a 60-degree angle.

1. How much force does the projectile experience before leaving the tube?
2. What is the mortar’s max height?
3. In order to get the firework to explode at the peak of its path, how long does the fuse need to burn?
4. The debris from the explosion is on average 20% of the firework’s initial mass. If we assume that the debris lands as a single mass and the water applies a 2-newton force upwards, how long does it take for the water to stop the debris?
5. How far away does the debris strike the water?