I am bored making up a worksheet so I needed to amuse myself. If you feel like grinding math here is a physics problem for you. All necessary information is given in one form or another.
Lini needs to reach a pool surrounded on all sides by Walls of Force. She casts water breathing on herself, while Ezren casts FLY. Ezren picks her up and flies towards the pool. After take off they fly at a height of 30 feet in the positive x direction. Ezren intends to drop Lini into the pool but where in his flight path should he drop her. (Assume graviity for Golarion is 32.2 ft/sec2)
I am bored making up a worksheet so I needed to amuse myself. If you feel like grinding math here is a physics problem for you. All necessary information is given in one form or another.
Lini needs to reach a pool surrounded on all sides by Walls of Force. She casts water breathing on herself, while Ezren casts FLY. Ezren picks her up and flies towards the pool. After take off they fly at a height of 30 feet in the positive x direction. Ezren intends to drop Lini into the pool but where in his flight path should he drop her. (Assume gravity for Golarion is 32.2 ft/sec2)
gravity = 9.81 m/s2 = 32.2 ft/s2
Setting 3D space
Y
X0
--Z
Y = +30
What are the dimensions of the pool?
How far away are they from the pool?
30feet tall wall, over 32 ft/s2 fall
so let go immediately at the top
I am bored making up a worksheet so I needed to amuse myself. If you feel like grinding math here is a physics problem for you. All necessary information is given in one form or another.
Lini needs to reach a pool surrounded on all sides by Walls of Force. She casts water breathing on herself, while Ezren casts FLY. Ezren picks her up and flies towards the pool. After take off they fly at a height of 30 feet in the positive x direction. Ezren intends to drop Lini into the pool but where in his flight path should he drop her. (Assume gravity for Golarion is 32.2 ft/sec2)
gravity = 9.81 m/s2 = 32.2 ft/s2
Setting 3D space
Y
X0
--ZY = +30
What are the dimensions of the pool.
Actually not needed:) We just need to know the time Lini is in the air.
Its 2d motion:) Projectile launched horizontally.
Assume it 10' X 10' though.
Any time we operate in 2d, we have only to worry about the X and Y components.
Vx=40 ft/sec (Ezren carrying light or medium load)
Vy=0
d=.5g X t2
Ezren intends to drop Lini into the pool but where in his flight path should he drop her. (Assume graviity for Golarion is 32.2 ft/sec2)
When he's directly over the pool, because there's no inertia in Pathfinder.
Ezren intends to drop Lini into the pool but where in his flight path should he drop her. (Assume graviity for Golarion is 32.2 ft/sec2)When he's directly over the pool, because there's no inertia in Pathfinder.
Inertia has to be assumed because of the jump skill rules and falling damage.
Ezren intends to drop Lini into the pool but where in his flight path should he drop her. (Assume graviity for Golarion is 32.2 ft/sec2)When he's directly over the pool, because there's no inertia in Pathfinder.Inertia has to be assumed because of the jump skill rules and falling damage.
Alright, sure, maybe Inertia is the wrong word. But a level 18 Monk can run 360' in one turn (that's ~41 miles per hour), stop on a dime, and run back in the opposite direction at the same speed.
He can charge 180 feet (that's ~20.5 miles per hour), stop completely in front of an enemy, and attack them without any risk of collision or impact or even extra damage (just a +2 to hit).
Further, this monk can actually move at 20.5 miles per hour through a twisting maze in which walls are never more than 5' apart, similarly with no risk of collision.
Slightly off-topic: Effects measured via radius have straight edges.
I am pretty sure I can just drop the guy over the pool.
(And yes, I fully recognize this was just supposed to be some math fun or whatever and that I just gave a smartass answer to be funny, which evidently failed).
Even if Ezren cast feather fall on Lini she would drop at a rate of 60 feet per round, so at an altitude of 30 feet all he needs to do is be over the water and she'll drop right into it on her turn. If he lets go sooner than that she will fall to right below where he is.
He would need to be much higher up in order to necessitate dropping her before he reached the edge of the wall, wouldn't he?
Although this does beg the question, how far do you fall in a round given that 1 round is 6 seconds? At a (rounded) rate of acceleration of 30 feet per second per second you would fall...how far? What is terminal velocity in ft/sec/sec? Just curious.
Never mind, I get what you're saying. Her forward inertia is 60 feet/3 seconds (assuming Ezren is continuing to fly in the same direction and doesn't stop to hover over the pool) or 20 feet/second, right? But that doesn't mean her horizontal speed continues to be that, does it?
I haven't taken physics in almost 25 years, but this rings a few bells hehe.
Assuming constant acceleration, a person would drop about 580 feet in one round.
You have to view this situation as a separate X vector and a Y vector.
Lini's initial speed in the X direction is 6.66 ft/sec (60 feet for fly-the light load she causes Ezren), 40 feet/rd=6.66 ft/sec Her initial speed in the Y direction is 0.
The horizontal distance would be 0 if she was released right on top of the pool. Timing is everything.
the distance from release to landing would be a function of the time she was in the air with the 40 feet speed (per second is wrong i realize).
Her horizontal distance (from release to landing) could be found by the equation S=d/t. As it stands this equation cannot be used because time is unknown.
The Y direction however has all the variables one needs to find time.
d=1/2*g*t2
30 = 16.1 * t2; t2=30/16.1=1.86
t= square root of 1.86=1.36 seconds
Lini is in the air for 1.36 seconds. Therefore if Ezren was above the pool, her horizontal velocity would carry her a good distance farther than the pool.
SO the point from when Ezren drops Lini she would travel a Distance = speed * time. 6.66 ft/seconds * 1.36 seconds. So Ezren must drop her 9 feet away.
I promise you I don't use this for rulings in my game.
The situation makes no sense, because they probably would never be in this situation in game. But have you ever read physics problems? The problems can almost always be overcome by saying I just walk over the bridge:)
Assuming constant acceleration, a person would drop about 580 feet in one round.
I like how the developers accounted for this in falling. If your falling greater than 500 feet you can get your normal amount of actions.
I have wasted serious campaign development time doing physics problems in rounds. For absolutely no reason.
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Lini needs to reach a pool surrounded on all sides by Walls of Force. She casts water breathing on herself, while Ezren casts FLY. Ezren picks her up and flies towards the pool. After take off they fly at a height of 30 feet in the positive x direction. Ezren intends to drop Lini into the pool but where in his flight path should he drop her. (Assume graviity for Golarion is 32.2 ft/sec2)
Smartass answer 1: Ezren level 7 has fly skill of 12 (possibly from the headband) - so from any level where he can cast the fly spell he can fly at any speed safely as long as he doesn't hover (DC 10 to fly at less than half speed and he can't get less than 11 at level 5). At a fly speed of 5ft it doesn't matter when he drops her she will still land within the same 5ft square.
Smartass answer 2: Never go in alone. Water breathing is a multi-target spell cast on them both. So Ezren flys over the target spot, hovers and then flies straight down into the water - as intended.
Physics answer: hmm, you need a lot of assumptions if you want a non-degenerate answer. But assuming lots of things:
Also Lini is a gnome and minimum weight for a female gnome means that Ezren is at medium or heavy load. Max fly speed = 40ft. Fly at 30ft for simplicity - minimum speed without requiring a fly roll.
Fall 30ft in about 1 and a third seconds
At 10ft per second travel 13-14 ft in 1 and a third seconds - or three five-feet squares.
So drop her 3 squares from target.
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Alright, sure, maybe Inertia is the wrong word. But a level 18 Monk can run 360' in one turn (that's ~41 miles per hour), stop on a dime, and run back in the opposite direction at the same speed.
He can charge 180 feet (that's ~20.5 miles per hour), stop completely in front of an enemy, and attack them without any risk of collision or impact or even extra damage (just a +2 to hit).
Further, this monk can actually move at 20.5 miles per hour through a twisting maze in which walls are never more than 5' apart, similarly with no risk of collision
The monk probably runs faster than his listed speed to take into account acceleration to and from speed and corners.
Assuming constant acceleration, a person would drop about 580 feet in one round.
That is good to know. Many thanks!
Fall 30ft in about 1 and a third seconds
At 10ft per second travel 13-14 ft in 1 and a third seconds - or three five-feet squares.
So drop her 3 squares from target.
I got 6 squares from target, but I was using double the horizontal movement (20 ft/s) because I didn't calculate Ezren's encumbrance from carrying Lini. Good call.
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Assuming constant acceleration, a person would drop about 580 feet in one round.That is good to know. Many thanks!
By the end of round one you reach terminal velocity (if in skydiver pose).
Second and subsequent rounds you fall around 1060 ft if you maximise your surface area/air resistance or around 1800 ft if you try to minimise your air resistance.