A 160kg astronaut (including space suit) acquires a speed of 2.80m/s by pushing

Question

A 160kg astronaut (including space suit) acquires a speed of 2.80m/s by pushing off with his legs from a 1700kg space capsule.

A) What is the change in speed of the space capsule?

  Express your answer with the appropriate units.

________________

B)

If the push lasts t = 0.485s , what is the average force exerted by each on the other? As the reference frame, use the position of the capsule before the push.

Express your answer with the appropriate units.

________________

C) What is the kinetic energy of the astronaut after the push?

Express your answer with the appropriate units.

_______________

D) What is the kinetic energy of the space capsule after the push?

Express your answer with the appropriate units.

______________

Explanation / Answer

mass of astronaut = Ma = 160 kg

mass of capsule = Mc = 1700 kg

before pushing , capsule and astronaut are together.

So total mass = M = 160 kg + 1700 kg = 1860 kg

Velocity of Capsule + astronaut before push = V =0

Velocity of astronaut after push = Va = 2.80 m/s

Velocity of capsule after push = Vc = ?

Total Momentum before push = Mtotal x V = 1860 kg x 0 = 0

Momentum of astronaut after push = Ma x Va = 160 x 2.80 m/s = 448 kgm/s

Momentum of capsule after push = Mc x Vc = 1700 x Vc m/s = 1700 Vc kgm/s

Using conservation of momentum :

Total Momentum before push = Momentum of astronaut after push + Momentum of capsule after push

0 = 448 kg m/s + 1700 Vc

Vc = -448 / 1700 = - 0.264 m/s

Vc = - 0.264 m/s in the opposite direction of astronaut

change in speed = final speed - initial speed = 0.264 m/s - 0 = 0.264 m/s

B) Change in momentum of capsule = Mc x Vc

using impulse momentum equation:

F = change in momentum / t = Mc Vc /t = - 1700 kg x (0.264 m/s) / (0.485 sec) = - 925.4 N

Average force = 925.4 N

C) Kinetic energy of astronaut = (0.5) Ma Va2 = (0.5) ( 160 kg) ( 2.80 m/s)2= 627.2 J

D ) Kinetic energy of capsule = (0.5) Mc Vc2 = (0.5) ( 1700 kg) ( 0.264 m/s)2 = 59.24 J

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