Catapults date from thousands of years ago, and were used historically to launch everything from stones to horses. During a battle in what is now Bavaria, inventive artillerymen from the united German clans launched giant spaetzle from their catapults toward a Roman fortification whose walls were 8.50 m high. The catapults launched spaetzle projectiles from a height of 4.60 m above the ground, and a distance of 40.3 m from the walls of the fortification at an angle of 60.0 degrees above the horizontal (see figure). The projectiles were to hit the top of the wall, splattering the Roman soldier atop the wall with pulverized pasta. (For the following questions, ignore any effects due to air resistance.)

(a) What launch speed was necessary?

m/s

(b) How long were the spaetzle in the air?

s

(c) At what speed did the projectiles hit the wall?

m/s