We are given this problem statement: the farthest distance for a human fired fro

Question

We are given this problem statement: the farthest distance for a human fired from a canon is 59.08 m and he was an 190 lb man. I need to have some research with calculations concerning the kinematic motion. Mainly I need info and calculations for the force and acceleration for the problem.
These are the variables I have so far: X distance = 250 ft Initial firing angle = 50.37 degrees Initial velocity = 20.37 Total distance G = 9.81 t= 4.33 s Vo= 27.57m/s y=23m X max= 76.2 m Vy=21.24m/s h=y

We are given this problem statement: the farthest distance for a human fired from a canon is 59.08 m and he was an 190 lb man. I need to have some research with calculations concerning the kinematic motion. Mainly I need info and calculations for the force and acceleration for the problem.
These are the variables I have so far: X distance = 250 ft Initial firing angle = 50.37 degrees Initial velocity = 20.37 Total distance G = 9.81 t= 4.33 s Vo= 27.57m/s y=23m X max= 76.2 m Vy=21.24m/s h=y


These are the variables I have so far: X distance = 250 ft Initial firing angle = 50.37 degrees Initial velocity = 20.37 Total distance G = 9.81 t= 4.33 s Vo= 27.57m/s y=23m X max= 76.2 m Vy=21.24m/s h=y

X distance = 250 ft Initial firing angle = 50.37 degrees Initial velocity = 20.37 Total distance G = 9.81 t= 4.33 s Vo= 27.57m/s y=23m X max= 76.2 m Vy=21.24m/s h=y

Explanation / Answer

as we get only air resistance here this is an example of projectile motion

the output we need is force and accleration

now the initial angle=50.37degrees

initial velocity =V=20.37ft/s

then in horizontal

Vx=Vcos(50.37)=20.37*.637=12.99ft/s

again in horizontal X=Vx.t

or 250=12.99*t

or t=19.24s

using V^2=U^2+2aS

we get 20.37^2=12.99^2+2*a*250

or a=.492ft/s^2

the horizontal force F=M*a=190*.492=93.48 lbf

for vertical component

Vy=Vsin(50.37)=20.37*.770=15.68ft/s

then Vf=Vy-g.t

or 0=15.68-32.2t

or t=.487sec

distance covered h=Vy.t-1/2gt^2

or h=15.68*.487-1/2*32.2*(.487)^2

or h=3.81ft

so, F=190*32.2lbf=6118lbf

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