Thursday, November 12, 2015

A Fall to Her... Safety?

While talking about our “bad movie physics” quiz, I started thinking about movies that I have seen recently that showed some questionable physics.  One movie I felt this was especially obvious in was The Pirates of the Caribbean: Curse of the Black Pearl. 

One scene in particular puzzled me.  In this scene, Elizabeth Swan (Keira Knightley) passes out from wearing a corset too tightly and falls from a ledge into the ocean.  After she is rescued from the water, she appears to have no injuries. My question was with what force did Keira Knightley hit the water and if she would actually have walked away with no injuries. 

From the clip, it was determined that the fall took roughly 3 seconds (00:37 to 00:40 in clip). I am treating her situation as if she was dropped off the ledge because she does not push off.  Her acceleration is only due to gravity.  I also assigned the downward direction as positive and the 0 reference height for PE is the surface of the water. From this information, I used kinematics to determine the height of the fall:
Δx = vot + ½ at2
Δx = ½ (9.8 m/s2) (3.0s)2
Δx = 44.1m (145ft)

To find out how much force she hit the water with, I used conservation of energy and ignored air resistance, therefore the expression for conservation of energy is:
PEo + KEo = PEf + KEf

Because she starts the fall from rest and the fall ends at the 0 height, both her initial KE and final PE are 0J.  This adjusts the conservation of energy expression to be:
PEo = KEf

Using my calculated height and estimating Keira Knightley’s weight to be approximately 120lbs or 54.4kg, I determined her initial potential energy to be:
PEo = mgh
PEo = (54.5kg)(9.8m/s2)(44.1m)
PEo = 2.4 x 104 J

Because PEo = KEf; 2.4 x 104J = KEf. 

I then used the work-energy principle to relate the kinetic energy to force needed to stop her in the water (d is estimated):
Wnet = Fdcosθ = ΔKE
F (1m)(cos0°) = 2.4 x 104 J
F = 2.4 x 104 N = 5,295 lb force

From this I can conclude that the probability of Keira Knightly having no injuries from this fall is very low and the physics of this scene are flawed. 

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