You've been hired as an apprentice engineer helping to design a circus act in which a performer is launched from a cannon and lands in a net that is at the same height above the ground as the cannon's exit point. The circus manager is demanding that the performer's maximum height is equal to half the total horizontal distance he travels, and you must determine at what angle the cannon must be oriented in order to make this happen. When you and the lead engineer ask for the speed at which the performer is launched from the cannon, the circus manager informs you that the speed is unknown because the amount of explosive powder used in the cannon varies from performance to performance. The next morning, you find that the lead engineer has hastily left the country leaving you to do all of the work; he was actually an English major who faked his transcripts because he thought he could get a better job in a STEM related field. The circus' first show is about to begin and the cannon launch is happening in a half hour. You're the only one who can calculate this angle, and the bearded lady is beginning to stare at you menacingly.
At what angle must the cannon be oriented so that the maximum peak height is equal to half the maximum horizontal distance traveled?
