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Nightmare on Calc Physics

Pirate, Ninja, Zombie, Robot Challenge

Lets say on a soccer field a pirate from rest at t=o (0,0,0) is running 4.5 m/s N 30 degrees East towards a zombie moving .5 m/s due East.

Image: My block chart of Calculus Physics study topics

(1) From the zombies perspective, what is the maximum angle beta the pirate, who is left handed, can swing through and not hit the parrot on his right shoulder when the pirate intercepts and attacks the zombie at time t?

(2) According to a incidental robot stationary at (-3, -4, 0) what is the minimum angle the pirate must rotate through at time t and strike the zombie?

(3) A ninja riding a bicycle leisurely 2.3 m/s, (7,4,0) at t_o due West notes to herself the pirate and zombie appear to have a total velocity q. Assuming acceleration is constant, What is (a) the average velocity of the ninja-pirate-zombie-robot system and (b) the minimum angle gamma the robot would see the pirate strike his parrot at time t if the pirate swung his sword too far?

(4) Neglecting air resistance, if the incidental robot decides at t_0 decided to drop kick a beer can at the pirate to startle the parrot, what must be the initial velocity if the robot kicks at phi degrees?

(5) Given the information, can the radius of the ninja's bike tires be defined?

(6) Given the information, could a balloonist define the (a) Ninja (b) Pirate (c) Zombie or (d) Robot as a target at time t_0>t for a water balloon mass m? (e) How about a plane dropping a package?

(7) The robot being drunk instead kicks at theta degrees at an initial velocity f (m/s) at t=0 and shatters a third story window (-8,6,z) meters from the pirate. (a) What can be said about the height z of the window? (b) Can it be determine if the ninja passes the window before the robot breaks it?

(8) Annoyed, a resident looks out the broken window and recognizes the zombie as it's grandmother. The resident shoots a poison dart striking the pirate in twice the time it took the robot to hit the window. Can it be determined if zombie grandmother been struck?

(9) The pirate turns out to be 3/4 the height of the resident's zombie grandmother. If the pirate hasn't been hit by the blowdart, when he attacks he has to adjust the angle of rotation of the sword. (a) Who's observational angles are effected? (b) If the pirate unstruck pirouettes to strike the zombie, as to not frighten the parrot, what can be stated about the centripetal force of about the sword, and (c) and the centripetal acceleration of the parrot? (d) What if the pirate really is the same height of the zombie?