On September 8, 2004, the genesis spacecraft crashed in Utah desert because it's parachute did not open. The 210-kg capsule hit the ground at 311 km/h and penetrated the soil to a depth of 81.0 cm.

1) Assuming it to be constant, what is its acceleration (in m/s^2) during the crash?

2) Assuming it to be constant, what is its acceleration (in g's) during the crash?

3) What force did the ground exert on the capsule during the crash? Express the force in newtons.

4) What force did the ground exert on the capsule during the crash? Express the force as a multiple of the capsule weight.

5) For how long did this force last?

Explanation:

mass of capsule, m = 210 kg

initial velocity, u = 311 km/h = 86.39 m/s

final velocity, v = 0 m/s

distance of soil penetrated, d = 81 cm = 0.81 m

1.

Let a is the acceleration.

Use third equation in motion.

v² = u² + 2as

0 = 86.39² + 2 x a x 0.81

a = - 4606.9

a = - 4607 m/s²

Thus, the acceleration during the crash is 4607 m/s².

2. g = 9.8 m/s²

a / g = 4607 / 9.8

a = 470 g

Thus, the acceleration is 470 g .

3. Force = m a

F = 210 x 4607

F = 967470 N

Thus, the force is 967470 N.

4.  Weight of capsule = m g = 210 x 9.8 = 2058 N

F / mg = 967470 / 2058

F = 470 times the weight of capsule.

5. Let t be the time.

Use first equation of motion.

v = u + at

0 = 86.39 - 4607 x t

t = 0.0188 second

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