Must show all work and especially accompany with FREE BODY DIAGRAMS!!! A man is

Question

Must show all work and especially accompany with FREE BODY DIAGRAMS!!!

A man is to be launched, as a cannonball and fired from a spring loaded cannon as shown. The object is to hit the target 600 ft downrange. The spring is to be compressed 5 ft. in the cannon prior to firing. Assume the man is 98 lb particle, neglect friction in the barrel of the cannon and the drag during his projectile flight motion. Find:

A) the required spring constant needed in the cannon for the man to reach the target.

B.) Whats the max g-force the man feels when he is launched from the cannon.

Explanation / Answer

s=ut+1/2*a*t^2

for horizontal direction

s=600ft

a=o

u=V*cos(30)

and

for t we need to consider veritcal direction

from v=u+a*tup

v=0

u=Vsin(30)

a=-g

t=2*tup=2*Vsin(30) / g

g=32.152231 ft/sec^2

where V speed of the man just after leaving spring

hence the s=V(cos(30)) * (2*Vsin(30) / g)

V=149.24 ft/s

1/2*m*V^2=1/2*k*x^2

k=(V/X)^2 * m

m=98 lb

x=5ft

k=87320.191

2)g force

k*x=m*a

a=138*g-g(for gravity in downwards)=137g upwards

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