An astronaut has drifted too far away from the space shuttle while attempting to

Question

An astronaut has drifted too far away from the space shuttle while attempting to repair the Hubble Space telescope. She realizes that the orbiter is moving away from her at 2 m/s. She and her space suit have a mass of 80 kg. On her back is a 10 kg jetpack which consists of an 8 kg holding tank filled with 2 kg of pressurized gas. She is able to use the gas to propel herself directly towards to the orbiter. The gas exits the tank at a uniform rate with a constant velocity of 100 m/s, relative to the tank (and her). (a) After the tank has been emptied, what is her velocity? Will she be able to catch up with the orbiter with that velocity? (b) With what velocity (in her frame of reference!) will she have to throw the empty tank away to reach the orbiter?

Explanation / Answer

Given Data

mass, m 1 = 80+10+8 = 98 kg

mass, m2 = 2 kg

u1 = 0

u2 = 0

v2 = 100 m/s

Let v1 = v

Solution :-

a) conservation of momentum

m1*u1 + m2*u2 = m1*v1 + m2*v2

98*0 + 2*0 = 98*v - 2*100

v = 2.04 m/s

so she can catch it

b)

so after she throws it we want her to have a speed of 2 m/s

98*2.041 = 100*2 + 8*(2.041 - v)

v = 2.041 m/s

(or)

a)
Let v is the velcoity gained by the her afetr the tank has been emtied.

Apply conservation of energy.

(80 + 8)*v = 2*100

v = 200/88

= 2.27 m/s

clealry, v > 2 m/s

so, she can catch the orbiter.

b) let v is the speed throgh which she should through the tank to cacth the orbiter.

Agaign apply conervation of momentum.

momentum gained by her = momentum gained by tank in the opposite direction.

80*2 = 10*v

==> v = 160/10

= 16 m/s

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