Atharva T.

Physics

As soon as the factory workers found out that a fire had occurred in the building, the staff in charge of evacuation cleverly guided the workers out from the top. There was just one problem- the height of the drop. Even though we had some brave workers, we still had to ensure their safety since the free-fall would affect the way the worker lands on the airbag. With a height of about 5 stories which is about 54.15 ft or 16.5 m. Still, the firefighters were quick with their response and promptly set a giant airbag below the building to safely catch all 4 of the workers(1st worker of 61kg who jumped straight down, 2nd worker of 55kg who ran towards the airbag at 2 m/s, 3rd worker of 49kg who jumped upward at a speed of 5 m/s and fell toward the airbag, and the 4th worker of 70kg who jumped upward at an angle of 20 deg at an upward speed of 5 m/s while running horizontally at 2 m/s without causing any kind of physical damage). The amount of force, kinetic energy, and velocity will be calculated to make sure that the person does not get harmed while also taking into consideration the force of the air from underneath the individual which lightens the impact into the airbag.

Calculations

For the 1st person the velocity that the person would go down with:

vyf^2=vyi^2+2(a)(delta y)

vyf^2=(0)^2+2(-9.8)(0-54.15)

vyf^2=1061.34

vyf=32.58 m/s

mass=61 kg, dropped straight down from height of 16.5m when acceleration of gravity(g)= -9.8 m/s^2 with upward air force of 10 N.

Sum of the forces in the x = m*ax

-(Fg)+(Fair)=mass*g

(Fg)+(10)=61*(-9.8)

Fg=587.8 N

Thus the person will have a kinetic energy of KE=1/2(m)(v)^2

KE=1/2(61)(32.58)^2

KE=32370.87 J

Thus, the 1st individual is safe since their velocity, kinetic energy, and force of gravity can be handled by the airbag.

 For the 2nd person, since they are running while jumping the velocity would be:

vyf^2=vyi^2+2(a)(delta y)

vyf^2=(0)^2+2(-9.8)(0-54.15)

vyf=32.58 m/s

Sum of Forces=ma

(-Fg)+(Fair)= ma

-Fg+10=55(-9.8)

Fg=529 J

For time

t^2=(yf-yi)/(.5)(a)

t^2=-54.14/(-4.9)

t= 3.3 seconds

For KE, 

KE=.5(m)(v)^2

=.5(55)(32.58)^2

= 29190.1 J

For the 3rd person,

actual height

vyf^2=vyi^2+2a(yf-yi)

0=5^2+2(-9.8)(yf-0)

yf=5.10 m+54.15= 59.25m

While the Force of Gravity on the worker

Sum of Forces=ma

-(Fg)+(Fair)= ma

-Fg+(10)=49(-9.8)

Fg=470.2 N

Final velocity at the end will be

Vyf^2=Vyi^2+2(a)(delta y)

Vyf^2=(0)^2+2(-9.8)(-59.25)

Vyf=34.1 m/s

thus the kinetic energy of the worker will be:

KE=(.50)(49)(34.1)^2

=28452.83 J

For the 4th worker, the person jumps at an angle of 20 deg at a horizontal speed of 2 m/s and upward speed of 5 m/s.

For the final velocity of the person at the moment when they land on the air, the initial velocity is 5 m/s which reduces to 0 when the individual jumps up to 59.25 m and drops down leading to the same calculations as the 3rd worker but the individual will certainly have a different kinetic energy and force of gravity as well

Force of Gravity

Sum of Forces=ma

-(Fg)+(Fair)= ma

-(Fg)+(10)=70(-9.8)

Fg=696 N

Kinetic Energy

KE=.5(m)(v^2)

KE=.5(70)(34.1)^2

KE=40646.9 J

The above calculated values show that the velocities, forces, and kinetic energies are not enough to cause significant damage to the workers. We truly have to thank our firefighters for acquiring such a flexible yet strong airbag for rescue missions!

Sources:

  1. Cross, Rod. “Forensic Physics 101: Falls from a Height.” Am. J. Phys. American Journal of Physics 76.9 (2008): 833. Web. 28 Mar. 2016.
  2. “Croydon Riots.” N.p., 28 Mar. 2016. Web.
  3. “Dangerous Jumping Calculator.” Dot Physics. N.p., n.d. Web. 28 Mar. 2016.
  4. “Jumping off a Building.” Physics Forums. N.p., n.d. Web. 28 Mar. 2016.
  5. “Speed of a Person Jumping off a Building?” Physics Forums. N.p., n.d. Web. 28 Mar. 2016.

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