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Falls resulting in hip fractures are a major cause of injury and even death to the elderly. Typically, the hip's speed at impact is about 2.0 m/s. If this can be reduced to 1.3 m/s or less, the hip will usually not fracture. One way to do this is by wearing elastic hip pads.

Part A

If a typical pad is 5.0 cm thick and compresses by 2.0 cm during the impact of a fall, what acceleration (in m/s2) does the hip undergo to reduce its speed to 1.3 m/s?

Part B

What acceleration (in g's ) does the hip undergo to reduce its speed to 1.3 m/s?

Part C

The acceleration you found in part A may seem like a rather large acceleration, but to fully assess its effects on the hip, calculate how long it lasts.
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s = v0t + (1/2)at^2
v = v0 + at and t = (v - v0)/a
s = v0(v - v0)/a + (1/2)a (v - v0)^2/a^2
2as = 2vv0 - 2v0^2 + (v^2 - 2vv0 + v0^2)
2as = v^2 - v0^2
v^2 = v0^2 + 2as

v0 = 2
v = 1.3
s = 2 cm = .02 m

1.3^2 = 2^2 + 2a(.02)
a = -57.75 m/s^2 = 5.893 g's

v = v0 + at = 2 - 57.75t = 1.3
t = .01212 seconds
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