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# Ancient Greek catapults and medical packs

## Problem

The Ancient Greeks were made famous for many reasons, including their martial engineering feats. Specifically, the legendary Archimedes designed a contraption that would throw large boulders, referred to as the Lithobolos.
The Lithobolos technology was later used by military personnel to catapult medical equipment to allied neighboring camps. This method was effective in reducing the amount of casualties, as no soldiers were compromised in the delivery of the aid, and the equipment itself was received faster than if it had been delivered on foot. This resulted in quicker and more efficient treatment of combat wounds, ultimately providing the civilization utilizing this technique with a military edge.
An engineer of one such nation is interested in improving the mechanics of the Lithobolos. He begins by launching medical packs of equal weight at different speeds and angles. The packs start at ground level, fly through the air, and land further in a flat practice field. The engineer measures the distance between launch point and landing point. He performs 5 trials and collects the following data:
Launch numberLaunch speed (meters/second)Angle of shot (degrees)Launch distance (meters)
1203035
24030141
3204040
44040161
5204541
Which calculation would give the vertical component of the launch velocity during launch trial 2?