A70-kg astronaut floating in space in a 110-kg mmu (manned maneuvering unit) experiences an acceleration of 0.029 m/s2 when he fires one of the mmu's thrusters. you may want to review (pages 258 - 260) . for related problemsolving tips and strategies, you may want to view a video tutor solution of acceleration of a rocket. if the speed of the escaping n2 gas relative to the astronaut is 490 m/s, how much gas is used by the thruster in 5.0s and what is the thrust of the thruster?

Answers:

a) 0.053 kg

b) 5.22 N

Explanation:

We have the following data:

is the mass of the astronaut

is the mass of the MMU

is the acceleration of the system astronaut-MMU

is the velocity of the ejected fuel

Now, we have the following two equations to find the amount of gas (mass) ejected by the thruster and the thrust :

(1)

(2)

Where:

is the total mass of the system astronaut-MMU

is the mass of the ejected fuel

is the time interval in which this occurs

Knowing this, let's begin with the answers:

a) How much gas is used by the thruster in 5s?

Here we have to isolate from (1) considering as constant, since the mass of the fuel is negligible compared to the total mass :

(3)

(4)

(5) Note the negative sign is because the direction of the ejected mass is opposite to the direction of the system astronaut-MMU. However, the value of is 0.053 kg.

b) What is the thrust of the thruster?

Let's use equation (2) with the calculated in (5):

(6)

Finally:

(7)

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