At a NASA research center free-fall research is performed by dropping experiment

Question

At a NASA research center free-fall research is performed by dropping experiment packages from the top of an evacuated shaft 149 m high. Free-fall imitates the so-called microgravity environment of a satellite in orbit. Hint: In this problem, all the motion is downward, so make the top y=0, and have the positive y-axis pointing downward.

(a) What is the maximum time interval for free fall if an experiment package were to fall the entire 149 m?

(b) Actual NASA specifications allow for a 5.21 s drop time interval. How far do the packages drop in 5.21 s?

(c) What is their speed at 5.21 s?

(d) NASA does not want the experiment package to slam into the ground and get smashed to pieces. They fill the bottom of the shaft with lightweight foam to break the fall. What constant acceleration would be required to gently stop an experiment package in the distance remaining in the shaft after its 5.21 s fall?

Explanation / Answer

PART a:

maximum time of travel is obtained from

H = 0.5 gt^2

t^2 = 2H/g

t^2 = 2* 149/9.81

t = 5.51 sec

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b. during a time if 5.21 s

height H = 0.5 gt^2

H = 0.5* 9.81* 5.21^2

H = 133.14 m

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c. v = u + gt

v = 9.81* 5.21

v = 51.11 m/s

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d. v^2 = 2 a s

here s = 149-133.14 = 15.86 m

accleration a = 51.11^2/(2* 15.86)

a = 82.35 m/s^2

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